Page 1 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 4, , MCSE-004, , MCA (Revised), O, c\1, O, , Term-End Examination, June, 2011, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, , Time : 3 hours, , Maximum Marks : 100, , Note : Question No.1 is compulsory. Attempt any three from, the rest. Use of calculator is allowed., 1., , (a) Define Absolute Error, Relative Error and 3+5, Percentage Error. Show that, (a — b), a, b, # — — — , where :, c, c c, a =0.41, b=0.36 and c = 0.70, (b) Find the real root of the equation, x3 — 2x — 5=0 using Bisection Method., Upto four iterations only., (c) Solve by Jacobi's method the following, system of linear equations., 2x1 — x2 + x3 = —1, X 1 + 2X2 - X3 = 6, x1 — X2 ± 2X3 - 3, Upto 3 - iterations only, , MCSE-004, , 1, , 8, , 8, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , Write down the polynomial of lowest degree, which satisfies the following set of numbers,, using the forward difference polynomial., , 8, , 0 1 2 3 4 5 6 7, f(x ) 0 7 26 63 124 125 342 511, x, , (e), , 8, , Evaluate, 1 1, —dx correct to 3 decimal places, 1+x, 0, by, (i), , Simpson's rule, (h =0.125), , Explain the cases where Newton's method, fail., , 4, , Find a real root of the equation, , 8, , f(x) = x3 – x –1 =0, Up to four iterations only., (c) Use Gauss - Seidel Method to solve the, equation :, x+y–z=0, –x+3y=2, x – 2z = –3, Initial solution vector is [0.8 0.8 2.11T., Upto 3 - iterations only., MCSE-004, , 2, , 8
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Download More:- https://www.ignouassignmentguru.com/papers, , 3., , (a) The population of a town in the decennial, census was as given below Estimate the, population for the year 1895., Year : x, , 8, , 1891 1901 1911 1921 1931, , Population : y, (in Thousands), , 46, , 66, , 81, , 93, , 101, , 6, , 4., , Evaluate, , [2 + sin(2J )dx using, 1, simpson's rule with 5 points., , 8, , Explain Euler's Method for solving an, ordinary differential equation., , 4, , (a) Solve the initial value problem d y = 1 + y2, dx, where y = 0 when x=0 using Fourth order, classical Runge-Kutta Method. Also find, y(0.2), y(0.4), , 10, , (b) Evaluate the integral I =, , 2 2xdx, , 1+x, , 4 using 10, , Gauss - Legendre 1 - point, 2 - point and, 3 - point quadrature rules. Compare with, the exact solution., 5., , (a) A box contains 6 red, 4 white and 5 black, balls. A person draws 4 balls from the box, at random. Find the probability that among, the balls drawn there is at least one ball of, each color., , MCSE-004, , 3, , 8, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , Find the most likely price in Bombay, corresponding to the price of Rs. 70 at, Calcutta from the following, , 8, , Calcutta Bombay, Av. Price, 65, 67, Standard Deviation, 2.5, 3.5, Corelation Co - efficient between the prices, of commodities in the two cities is 0.8., (c), , MCSE-004, , Ten coins are thrown simultaneously. Find, the probability of getting at least seven, heads., , 4, , 4
Page 5 :
Download More:- https://www.ignouassignmentguru.com/papers, , I MCSE-004 1, , No. of Printed Pages : 3, , MCA (Revised), , C\1, oo, , Term-End Examination, December, 2011, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note :, , 1., , Question No. 1 is compulsory. Attempt any three from, the rest. Use of calculator is allowed., 2+6, , (a) Define Error., equation, quadratic, Solve, the, x2 + 9.9x —1= 0 using two decimal digit, arithmetic with rounding., (b), , Use Bisection Method to find a root of the, , 8, , equation x3 — 4x — 9=0. Go upto 5 iteration, only., (c), , Solve the equations :, , 8, , 2x+3y+z =9, x+2y+3z =6, 3x+y+2z=8, by LU decomposition Method., , MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d) From the following table. Find the value of, e1.17,, using backward interpolation formula., X, , 1.00, , 1.05, , 1.10, , 1.15, , 1.20, , ex, , 2.7183, , 2.8577, , 3.0042, , 3.1582, , 3.3201, , 8, , 6, , (e) Evaluate the integral ( x2+x+2) dx using, 0, Trapezoidal rule with h = 1.0, 2., , (a) Find a real root of the equation, , 8, , 10, , x3 +x2 -1 =0, on the interval [0,1] using successive, iteration method, upto three iterations only., (b) Use Gauss Elimination to solve the system 10, of equations., 10x1 — 7x2 = 7, — 3x1 + 2.099x2 + 6x3 = 3.901, 5x1 — x2 + 5x3 = 6, upto 3 iterations only., 3., , (a) Use Runge - Kutta method to solve the initial 10, value problem., = (t — y)/2 on [0,0.2] with y(0) =1., Compare the solutions with h = 0.2 and 0.1., P/2, , (b), , Evaluate the integral I=, , J0 sin x dx, , Using the Gauss-Legendre formulas., Compare with the exact solution (the exact, value is I = 1)., , MCSE-004, , 2, , 10
Page 7 :
Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a) Find the Lagrange interpolating polynomial, of degree 2 approximating the function, y =ln x defined by the following table of, values. Hence determine the value of In 2.7., , 10, , 3.0, 2.5, y = In x 0.69315 0.91629 1.09861, Also estimate the error in the value of y., X, , 2, , J [2+sin(2 rx)] dx, 6, , (b), , 10, , Evaluate the above integral using, trapezoidal rule with 5 points., 5., , (a) A manufacturer of cotter pins knows that, 5% of his product is defective. If he sells, cotter pins in boxes of 100 and guarantees, that not more than 10 pins will be defective., What is the approximate probability that a, box will fail to meet the guaranteed, quality ?, (b) Find the most likely price in Bombay, corresponding to the price of Rs. 70 at, Calcutta from the following :, Average price, Standard, Deviation, , (c), , MCSE-004, , 8, , 8, , Calcutta Bombay, 67, 65, 3.5, 2.5, , Correlation coefficient between the prices, of commodities in the two cities is 0.8., Show that the moment generating function, of a random variable x which is chi - square, distributed with v degrees of freedom is, M(t) = (1— 2t) —V / 2., , 3, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004, , MCA (Revised), Term-End Examination, , 07337, , June, 2012, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question No. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is allowed., 1., , (a) If 0.333 is the approximate value of 1/3, find, absolute, relative and percentage error., , 3, , (b), , Determine the number of iterations required, to obtain the smallest positive root of, x3 - 2x - 5 = 0 correct upto two decimal, places., , 5, , (c), , Solve x + 2y + z = 3, , 5, , 2x + 3y + 3z = 10, 3x - y + 2z = 13, by Gauss Elimination Method., (d), , MCSE-004, , Find the value of Atan-lx, the interval of, differencing being h., 1, , 2, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (e), , A table of x Vs. f (x) is given below. Find, the value of f (x) at x = 4, use Lagrange, Interpolation formula., 6, 3, x, 20, 2, f (x )-) — 0.25, , 5, , 0.6, , (f), , (g), , (h), , Find the value of J ez dx, taking n=6,, 0, correct to five significant figures using, Simpson's Y3 rule, An individual's IQ score has a Normal, distribution N (100, 152). Find the, probability that an individual IQ score is, between 91 and 121., Following data is given for marks in subject, A and B of a certain examination., Subject A Subject B, 85, 36, Mean Marks, 8, 11, Standard Deviation, , Coefficient of correlation between, A and B = ± 0.66, (i) Determine the two equations of, regression., (ii) Calculate the expected marks in A, corresponding to 75 marks obtained, in B., (i) Write the probability distribution formula, for Binomial distribution, Poisson, distribution and Normal distribution., MCSE-004, , 2, , 5, , 5, , 7, , 3
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Download More:- https://www.ignouassignmentguru.com/papers, , 2., , 3., , (a) Find an approximate value of the root of the, equation x3 + x –1=0, near x=1. Using the, method of Regula-Falsi, twice., (b) Solve following system of equations by using, Gauss - seidel iteration method, perform two, iterations, 8x – 3y + 2z = 20, 6x + 3y + 12z = 35, 4x + lly – z = 33, (c) Solve the following system of equations by, using LU decomposition method, x+y=2 ; 2x+3y=5, (d) For x = 0.5555 El ; y =0.4545 El and, z = 0.4535 El, prove that x (y – z) # xy – xz, , 5, , (a) A polynomial passes through the points, (1, –1), (2, –1), (3, 1) and (4, 5). Find the, polynomial using Newton's forward, interpolation formula., (b) Calculate the value of the integral, , 5, , 52, f log, 4, , (c), , 6, , 3, , 5, , x dx., , by using : (i) Simpson's 3 rule, (ii) Simpson's Y3 rule, Using Runge Kutta method find y (0.2) for, d y – y–x, dx y±x ; y(0)=1. Take, the equation —, h = 0.2., , MCSE-004, , 6, , 10
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Download More:- https://www.ignouassignmentguru.com/papers, , 4,, , (a) The tangent of the angle between the lines, of regression y on x and x on y is 0.6 and, 1, crx = 2.ay. Find r, , 5, , (b) Compute R and R2 for the data given below :, , 5, , Sample Size (i) 12 21 15 1 24, 0.96 1.28 1.65 1.84 2.35, xi, 138 160 178 190 210, yi, A, , y1, A, , ei, , 138, 0, , regression equation y = 90 + 50x is used to, fill the table where eA = yi — yAi ., , 5., , (c), , If a bank receives on an average A =6 bad, cheques per day. What is the probability, that it will receive 4 bad cheques on any, given day ?, , 5, , (d), , What do you mean by term "Goodness to, fit test" ? What for the said test is required?, , 5, , (a) Solve the following system of equations by, Jacobi Method, determine the results for, three approximations., , 7, , 3x+4y+15z=54.8, x + 12y + 3z =39.66, 10x +y — 2z = 7.74, MCSE-004, , 4, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 1, , (b), , dx, Evaluate the integral I=0 1+x by using, , 8, , composite trapezoidal rule with 2 and 4, subintervals., (c), , A book contains 100 misprints distributed, randomly throughout its 100 pages. What, is the probability that a page observed at, random contains atleast two misprints., , MCSE-004, , 5, , 5
Page 13 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004, , MCA (Revised), Term-End Examination, , 08086, , December, 2012, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question number 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is allowed., , 1., , 22, (a) If Tr = — is approximated as 3.14, find the, 7, , 3, , absolute error, relative error and relative, percentage error., (b), , Determine the real root of the equation, x3 — x2 — 2=0, correct to one decimal place,, using Regula-Falsi method., , 6, , (c), , Solve the following system of equations by, Jacobi iteration method., , 6, , 8x —3y + 2z =20, 4x +11y — z =33, (Perform three iterations) 6x + 3y +12z = 35, , MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d) Prove that A { log f (x) } = log, , 1-1+Af (x), [ f (x), , (e) Determine the polynomial in x, by using, Lagrange's interpolation, from the following, data., x, y= f (x, , ), , 0, -18, , 1, 0, , 3, 0, , 5, -248, , 6, 0, , 3, 6, , 9, 13104, , 5, , (f), , Find the value of logic) x dx, taking B, , 6, , subintervals correct to four decimal places, by Trapezoidal rule., (g), , The length of metallic strips produced by a, machine has mean 100 cm and variance, 2.25 cm. Only strips with weight between, 98 and 103 cm are acceptable. What, proportion of strips will be acceptable ? You, may assume that the length of a strip has a, Normal Distribution., , 6, , (h), , What do you mean by term "Random, Variable", classify them ? How you analyse, which probability distribution is applicable, on which type of random variable ?, , 4, , MCSE-004, , 2
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Download More:- https://www.ignouassignmentguru.com/papers, , 2., , (a) Verify that propagated error in addition is, given by, , 3, , x, y, ex+y =r x x±y +ry, x+y, where rx and r are relative error., (b), , The quadric equation x4 — 4x2 + 4 = 0 has a, double root. Starting with xo =1.5 compute, two iterations by Newton Raphson method., , 6, , (c), , Solve the linear system of equations, , 8, , 10 X1 X2 4- 2X3 — 6, — + 11X2 — X3 ± 3X4 = 25, 2X1 — X2 ± 10X3 — X4 = —11, 3X2 — X3 +8X4 = 15, by Gauss Seidel method rounded to four, decimal places., (d) Let a = 0.41, b = 0.36 and c = 0.70 prove, (a—b) #, b, # —, c, c, c, 3., , (a) Find Newton's Backward Difference form, of interpolating polynomial for the data :, 4, x :, f (x ) : 19, , 8, 79, , 6, 40, , Hence interpolate f (9)., MCSE-004, , 3, , 10, 142
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Download More:- https://www.ignouassignmentguru.com/papers, , 52, , (b), , 6, , x dx, Calculate the value of integral J log, 4, , by using, (i), (c), , Trapezoidal Rule (ii) Weddle's Rule, 8, , Solve the Intermediate Value Problem, (IVP) Y' = 2Y + 3e t ; Y(0) = 0 by using, Classical Runge - Kutta method of 0 (h 4)., Find Y (0.1), Y (0.2), Y (0.3) using h= 0.1., , 4., , 8, , (a) 1000 light bulbs with a mean life of 120 days, are installed in a new factory and their, length of life is normally distributed with, standard deviation of 20 days., (i), , How many bulbs will expire in less, than 90 days ?, , (ii), , If it is decided to replace all the bulbs, together, what interval should be, allowed between replacements if not, more than 10% should expire before, replacement ?, , (b) In partially destroyed laboratory record of 12, an analysis of correlation data, the, following results are legible, Variance of X = 9, Regression Equations : 8X-10Y +66=0, 40X — 18Y — 214 = 0, MCSE-004, , 4, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , What are :, (i), , the mean values of X and Y, , (ii), , the correlation coefficient between, X and Y, , (iii) standard deviation of Y., 5., , (a) What do you mean by the term "Accuracy", and "Precision", how they are related to, significant digits ?, 1, , Ax, , (b) Evaluate 5, using, 0 1+x, , (c), , 8, , (i), , Composite Trapezoidal rule, , (ii), , Composite Simpson rule with 2 and 4, subintervals., , Fit a straight line to the following data, regarding x as the independent variable :, x:, y:, , 0, 1.0, , 1, 1.8, , 2, 3.3, , 3, 4.5, , 4, 6.3, , Hence find the difference between the actual, value of y and the value of y obtained from, the fitted curve when x =3., , MCSE-004, , 4, , 5, , 8
Page 18 :
Download More:- https://www.ignouassignmentguru.com/papers, , MCSE-004, , No. of Printed Pages : 5, , MCA (Revised), Term-End Examination, , 09427, , June, 2013, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time 3 hours, , Note : Question number 1 is compulsory. Attempt any three, questions from the rest. use of calculator is allowed., , 1., , (a) Explain briefly what are the sources of 4+4, error ? Verify the associative property for, the floating point numbers. i.e. prove :, (a + b) — c # (a — c) + b, where a = .5665E1,, b = .5556E —1 and c = .5644E1, (b), , Find the root correct to three decimal places, using Regula - Falsi method x4 — x —10 = 0., , (c), , Solve the following system of equations, , 8, , 4x1 + x2 + x3 = 4, + 4x2 — 2x3 = 4, 3x1 + 2x2 — 4x3 = 6, By the Gauss Elimination method with, partial pivoting., MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , Find the unique polynomial P(x) of degree, 2 or less such that, , 8, , P(1)=1, P(3) =27, P(4)=64, Using Lagrange interpolation formula., (e), , Calculate the value of the integral, , 8, , 5.2, , log x dx, 4, , by, , 2., , (i), , Trapezoidal rule, , (ii), , 1, Simpson's — rule, 3, , (a) Find all the roots of cosx — x2 —x = 0 to five, decimal places., , 8, , (b), , 8, , Solve the following system of equations, , x+y—z=0, —x+3y=2, , x — 2z = —3, By Gauss - Seidel method. Write its matrix, form., (c), , MCSE-004, , Write the pitfalls in the Gauss Elimination, Method., 2, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , the, of which, (a) In the table below the values, of y are, , 3., , consecutive terms of a series, number 21.6 is the 0-11 term. "find the First, f the series., and tenth terms o, 5, , A 2 1,15ii-vg,weacker, ax, l x(b) -Evaluate the integra 1, -= 0.5, rule with h ..- 2, - V — x Where '9(0) a:9 =-ax ancl y(0.2) correct to four decimal, c.) Given, ind '9(0), , 7, , places using Runge-Kutta Second Order, Method ., An experiment consist of three independent tosses, , S, , of a fair C0111. - the no. of heads, (a) Let x ------ the no. of head Tuns, ii -,-----the length of head runs, Z run being defined as consecutive, a head, occurance of at least two heads, its length, then being, the number of heads occuring, togetlAer in three tosses of the coin. Find the, ction of, probability fun, 0-I) .9,, (1\1) % k, 0 %,, (iii) Z, 3, , MC5E-004
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Download More:- https://www.ignouassignmentguru.com/papers, , (b) In partially destroyed lab record of an, analysis of correlation data, the following, , 8, , results only are legible :, Variance of x = 9, Regression Equations, 8x —10y + 66 = 0, 40x — 18y = 214, What are :, (i), , The mean values of x and y, , (ii), , The correlation coefficient between, x and y., , (iii) The standard deviation of y ?, (c) A bag contains 6 white and 9 black balls, .Four balls are drawn at a time. Find the, probability for the first draw to give 4 white, and the second to give 4 black balls in each, of the following cases :, , MCSE-004, , (i), , The balls are replaced before the, second draw., , (ii), , The balls are not replaced before the, second draw., 4, , 4, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 5., , (a) Solve the initial value problem to compute, approximation for y(0.1), y(0.2) using, Euler's material with h = 0.1, , 10, , dy, _, 2y = 3e-4t , y(0) = 1, dt +, Compare with exact solution, , 5e-2t - 3e-4t, y(t) —, , 2, A, r x, u, , 1, , (b) Evaluate the integral, , MCSE-004, , J, , x using, , (i), , Composite trapezoidal rule, , (ii), , Composite simpson's rule with 2, 4, and 8 equal subintervals., , 5, , 10
Page 23 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 3, , MCSE-004, , MCA (Revised), Term-End Examination, , C40, , December, 2013, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question number 1 is compulsory. Attempt any three, from the rest. use of calculator is allowed., 1., , (a) Verify the distributive property of floating 5+3, point numbers i.e. prove :, a(b-c) # ab-ac a=.5555E1, b=.4545E1,, c=.4535E1, Define : Truncation error, Absolute Error, and Relative Error., (b) Find the real root of the equation x=e-x using 4+4, Newton-Raphson Method. List the cases, where Newton's Method fail., (c) Solve by Gauss-Seidel Method, 8, 2x1 — x2 + x3 = —1, X1 4- 2X2 - X3 = 6, — X2 ± 2X3 = - 3, Correct to 3 decimal places., (d) Let f(x)= ln(1 +x), x0=1 and x1=1.1 use, 8, linear interpolation to calculate an, approximate value of f(1.04) and obtain a, bound on the truncation error., , MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (e) Conside initial value problem, , 8, , dy, — = x + y; y(0) = 1, dx, Find y(0.2) using Runge-Kutta Method of, fourth order. Also compare it with exact, solution y=-(1+x)+2ex to find the error., 2., , 3., , (a) Find the interval in which the smallest, positive root of the following equation lies, using Bisection Method x3 – x –4 =0., (b) Solve the following linear system of, equations using Gauss Elimination method., x1+ x2 + x3 = 3, 4x1 + 3x2 + 4x3 = 8, 9x1 + 3x2 + 4x3 = 7, (c) Give properties of polynomial equations., , 8, , (a) The table below gives the values of tanx for, 0.1(Xx0.30, , 8, , 8, , 4, , 0.10 0.15 0.20 0.25 0.30, X, y= tan x 0.1003 0.1511 0.2027 0.2553 0.3093, Find (i), (b) Evaluate, 1, , tan0.12, , (ii), , tan0.26, 8, , 1, , x dx, correct to three decimal, 0, places. Using, (i) T rapezoidal and, (ii) Simpson's rule with h = 0.5 and, h = .25, (c) Determine the value of y when x = 0.1 given, that y(0) =1 and y1 = x2+ y, =, , MCSE-004, , 2, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a) A problem in statistics is given to the three, students A, B and C whose chances of, 13, 1, 1 and-i- respectively. What, 2 ,76solving it are —, , (b), , (c), , is the probability that the problem will be, solved., Calculate the correlation coefficiant for the, following heights (in inches) of fathers (x), and their sons (y) :, x : 65 66 67 67 68 69 70, y: 67 68 65 68 72 72 69, Three identical bags have the following, proportion of balls ., First bag : 2 black 1 white, Second bag: 1 black 2 white, Third bag : 2 black 2 white, One of the bag is selected and one ball is, drawn. It turns out to be white. What is the, probability of drawing a white ball again., The first one not been returned ?, , 6, , 8, , 6, , 6, , 5., , (a) Evaluate, , f [2 + sin(2,c)] dx, , using 10, , Simpsons rule with 11 points., (b) Estimate the sale of a particular quantity for 10, 1966 using the following table, Year :, 1931 1941 1951 1961 1971 1981, Sale in, 12 15 20 27 39 52, thousands :, , MCSE-004, , 3
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 4, , MCSE-004, , MCA (Revised), Term-End Examination, , O, , June, 2014, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, , Time : 3 hours, , Maximum Marks : 100, , Note : Question number 1 is compulsory. Attempt any three, questions from the rest. Use of calculators is allowed., 1., , (a) Determine the root of the equation, 2x = cos x + 3 correct to three decimal places., (b) Solve the following system of equations by, using Gauss Elimination method., , 5, 5, , 2x+ y+ z =10, 3x + 2y + 3z = 18, x + 4y + 9z = 16, (c), , Using Lagrange interpolation, determine the, value of log10 301, from the tabulated data, , 5, , given below :, X, 300, 304, 305, 307, logio X 2.4771 2.4829 2.4843 2.4871, MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , (e), , (f), , (g), , (h), , 2., , Ten coins are thrown simultaneously, Find, the probability of getting at least seven, heads., What do you mean by "Goodness to, fit test" ? What for the said test is, required ?, Calculate the value of the integral, 52, J log xd x by using Simpsons 3/8 rule, 4, Find the probability that an individual's, IQ score is between 91 and 121. Provided,, the individuals IQ score has a Normal, distribution N (100, 152)., Write short note on following :, (i) Non Linear Regression, (ii) Acceptance Rejection Method, , (a) Determine the value of expression, , 5, , 5, , 5, , 5, , 5, , 5, , X = -fi- + ,/- + -\/ ;, , (b), , (c), , (d), , MCSE-004, , accurate up to 4 significant digits, also find, the absolute and relative errors., Determine the value of Y using Euler's, method, when X ---- 0.1 Given Y(0) =1 and, Y'=X2 +Y., Find the value of A tan -1 x, where A is the, difference operator, with differencing step, size 'h'., Solve the following system of equations by, using LU Decomposition method., x+y=2 ; 2x+3y=5, 2, , 5, , 3, , 7
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Download More:- https://www.ignouassignmentguru.com/papers, , 3., , (a) Solve the initial value problem given below,, By using Runge - Kutta Method., dy, = y — x with y(0) = 2 and h= 0.1, dx, also find y(0.1) and y(0.2) correct to four, decimal places., (b) Determine the Goodness to fit parameter 'R', for the data given below., , 10, , 10, , X 100 110 120 130 140 150 160 170 180 190, Y 45 51 54 61 66 70 74 78 85 89, , Analyse the results and comment on, whether the predicted line fits well into the, data or not., 4., , (a) Develop the difference table for the data, given below and use it to find the first and, tenth term for the given data., , 10, , X, Y, , 3 4, 5, 6, 7, 8, 9, 2.7 6.4 12.5 21.6 34.3 51.2 72.9, (b) Find the smallest root of the equation, f(x) = x 3 — 6x 2 + 11x — 6 = 0 by using, Newton - Raphson method. Give two, drawbacks of Newton - Raphson method., 5., , (a) In a partially destroyed laboratory record, of an analysis of correlation data, the, following data are only legible :, (i) Variance of X = 9, (ii) Regression equation :, 8X — 10Y + 66 = 0, 40X — 18Y = 214, , MCSE-004, , 3, , 10, , 10, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , Using this legible data determine the, following :, (i), Mean value of X and Y, (ii), Correlation coefficient between, X and Y, (iii) Standard Deviation of Y, by using, , 5, , composite Trapezoidal rule with 2 and 4 sub, intervals., Find the approximate value of the root of, the equation x3 + x —1=0, near x =1. Using, Regula-Falsi method, twice., , 5, , (b) Evaluate the integral I —, , (c), , MCSE-004, , 4
Page 30 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 4, , MCSE-004, , MCA (Revised), Term-End Examination, December, 2014, , 1654, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, , Time : 3 hours, Note :, , Maximum Marks : 100, , Question number 1 is compulsory. Attempt any, three questions from the rest. Use of calculator is, allowed., , 1. (a) Find the value of 'e', correct to 3 decimal, 1, 1 +—, 1, places. e = 1 + —, +—, +, 2! 3! 4!, (b) If 0.333 is the approximate value of 1, –3 , find, absolute, relative and percentage error., Explain how these errors measure, accuracy., (c), , (d), MCSE-004, , 5, , 5, , If a bank receives on an average six bad, cheques per day, then what is the, probability that it will receive four bad, cheques on any given day ?, , 5, , Use the Newton-Raphson method to find a, root of the equation x3 – 2x – 5 = 0., , 5, , 1, , P.T.O.
Page 31 :
Download More:- https://www.ignouassignmentguru.com/papers, , (e) Find the value of sin(n/6) by using, Lagrange's interpolation, the related data, is given below :, x, y = sin(x), , Tr/4, :0, 0 0.70711, , 5, , It/2, 1.0, , f) Find the roots of the equation, e x— 5x + 2, by using Secant, f(x) = 2, , (g), , method., , 5, , The tangent of the angle between the, lines of regression y on x and x on y is 0.6, 1, and a x= — ay.Find rxy•, , 5, , (h) Evaluate dx, using Composite Trapezoidal rule with, n = 2 and 4., 2. (a) Show that the moment generating function, of a random variable X which is chi-square, distributed with v degrees of freedom is, M(t) = (1 —, , v/2, , (b) An irregular six faced die is thrown and, the expectation that in 10 throws it will, give five even numbers is twice the, expectation that it will give four even, numbers. How many times in 10,000 sets, of 10 throws would you expect it to give no, even number ?, MCSE-004, , 5, , 10
Page 32 :
Download More:- https://www.ignouassignmentguru.com/papers, , (c) Write short notes on the following :, (i), , 4, , Acceptance-Rejection method, , (ii) Non-Linear Regression, 3. (a) Solve by Jacobi's method, the following, system of linear equations :, 2x1 — x2 + x3 = — 1, x1 + 2x2 — x3 = 6, X1 — X2 + 2X3 = — 3, , 7, , n/2, , f, , (b) Evaluate the integral I = sin x dx using, 0, Gauss-Legendre formula. Compare the, results with exact solution obtained by, 10, Simpson rule. The exact value of I = 1., (c) What are the pitfalls of Gauss-Elimination, method ?, 4. (a) Write short notes on the following, Probability Distributions :, (i) Binomial Distribution, (ii) Poisson Distribution, (iii) Normal Distribution, (b) A polynomial passes through the following, set of points :, x, , 1, , 2, , 3, , 4, , y, , —1, , —1, , 1, , 5, , 3, 6, , Find the polynomial, using Newton's, 6, forward interpolation., P.T.O., 3, MCSE-004
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Download More:- https://www.ignouassignmentguru.com/papers, , (c), , Prove that x(y — z) # xy — xz, where, x = 0.5555 El, y = 0.4545 El and, z = 0.4535 El., , (d) Solve the quadratic equation, x2 + 9.9x — 1 = 0, using two decimal digit, arithmetic with rounding., 5. (a) Consider the following data and perform, the "Goodness of fit test" over it :, x 100 110 120 130 140 150 160 170 180 190, y 45 51 54 61 66 70 74 78 85 89, Now comment, whether the data is fitted, well or not., , 6, , (b) Use Runge-Kutta method to solve the, initial value problem y' = (t — y)/2 on, [0, 0.2] with y(0) = 1. Compare the solution, with h= 0.2 and h = 0.1., , 8, , (c), , 1, is, Evaluate the integral I = dx by using, 1+x, 0, Simpson's 1 rule with h = 0.25 (or, 3, , 5 points, viz. 0.0, 0.25, 0.50, 0.75 and 1.00)., , MCSE-004, , 4, , 6, , 10,000
Page 34 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004, , MCA (Revised), Term-End Examination, , 09603, , June, 2015, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question number 1 is compulsory. Attempt any, three questions from the rest. Use of calculators is, allowed., , 1. (a) Show that a(b — c), ab — ac, where, a = 0.5555 x 10 1 , b = 0.4545 x 10 1 and, c = 0.4535 x 10 1 ., Use 4-digit precision floating point and, significant digit rounded off., , 4, , (b) Solve the following linear system of, equations using Gauss Elimination method, with partial pivoting :, , 6, , x1 + x2 + x3 = 3, 4x1 + 3x2 + 4x3 = 11, 9x1 + 3x2 + 4x3 = 16, MCSE-004, , 1, , P.T.O.
Page 35 :
Download More:- https://www.ignouassignmentguru.com/papers, , (c), , (d), , Estimate the missing term in the following, data using forward differences :, x:, , 1, , 2, , f(x) :, , 3, , 7, , Evaluate, , the, , 3, , integral, , 4, , 5, , 21, , 31, , 4, f X 2 dx, , using Simpson's 1/3 rule with h = 0.5., , (e), , 6, , 4, , A filling machine is set to pour 952 ml of oil, into bottles. The amount to fill is normally, distributed with a mean of 952 ml and a, standard deviation of 4 ml. Use the, standard normal table to find the, probability that the bottle contains oil, between 952 and 956 ml., , (f), , What is the utility of residual plots ? What, is the disadvantage of residual plots ?, , (g), , If, , it =, , 314159265, then find out to how, , many decimal places the approximate, value of 22/ 7 is accurate., MCSE-004, , 4, , 2, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , (h), , Three bags of same type have the following, balls :, Bag 1 : 2 black 1 white, Bag 2 : 1 black 2 white, Bag 3 : 2 black 2 white, One of the bags is selected and one ball is, drawn. It turns out to be white. What is, the probability of drawing a white ball, again, the first one not having been, returned ?, , (i), 2., , 2, , Define Poisson Distribution., , (a) Find the smallest positive root of the, quadratic equation, x2 — 8x + 15 = 0,, using Newton-Raphson method., (b), , Find, , the, , Lagrange, , interpolating, , polynomial of degree 2 approximating the, function y = in x. Hence determine the, value of In 2.7. Also find the error., , (c), , x, , 2, , 2.5, , 3.0, , y = in x, , 0-69315, , 0.91629, , 1.09861, , What are the sources of errors in numerical, data and processing ? How does error, , MCSE-004, , measure accuracy ?, , 4, , 3, , P.T.O.
Page 37 :
Download More:- https://www.ignouassignmentguru.com/papers, , 1, 3., , dx, 1+x, , (a) Evaluate the integral I =, 0, , using Gauss-Legendre three-point formula., (b), , Solve the initial value problem u' = — 2t u 2, withu(0)=1and.2otheirvl, [0, 1]. Use the fourth order classical, Runge-Kutta method., , (c), , Evaluate, , 6, , f, , { 2 + sin (2120 dx, , 1, , using Composite Simpson's rule with, 5 points., 4., , (a) Calculate the correlation coefficient for the, following heights (in inches) of fathers (X), and their sons (Y) :, X:, , 65, , 66, , 67, , 67, , 68, , 69, , 70, , 72, , Y:, , 67, , 68, , 65, , 68, , 72, , 72, , 69, , 71, , Obtain the equations of lines of regression., Also estimate the value of X for Y = 70., , 10, , (b) A manufacturer of cotter pins knows that, 5% of his product is defective. If he sells, cotter pins in boxes of 100 and guarantees, that not more than 10 pins will be, defective, what is the approximate, probability that a box will fail to meet the, guaranteed quality ?, , 10, , MCSE-004, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , 5. (a) What do you mean by pseudo-random, number generation ? What is the practical, advantage of the concept of random, number generation ?, (b), , For the data given in the table, compute R, and R2, where R denotes S xy, , xx yy, , Sample, No (i), , 12, , 21, , Xi, , 0.96, , 1.28, , 1.65 1.84, , 2.35, , Y1, , 138, , 160, , 178, , 210, , 9i, , 138, , A, , e .1, , 15, , 1, , 190, , 10, , ., , 24, , 0, , Note : 9 i = 90 + 50 Xi and e i = Yi - 9 i ,, A, , A, , for calculating y and e ., (c), , MCSE-004, , If a bank receives on an average X = 6 bad, cheques per day, what is the probability, that it will receive 4 bad cheques on any, given day, where A, denotes the average, arrival rate per day ?, , 5, , 8,000
Page 39 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004, , MCA (Revised), , 0 6 0 0.4, , Term-End Examination, December, 2015, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question number 1 is compulsory. Attempt any, three questions from the rest. Use of non-scientific, calculator is allowed., , 1., , (a) Solve, , the, , quadratic, , equation, , 4x2 + 8x — 21 = 0 using two decimal digit, arithmetic with rounding, using any one of, the following methods :, (i), , Regula-Falsi, , (ii), , Secant, , (iii) Bisection, , 6, , (b) Round off the number 4.5126 to 4, significant figures and find the relative, percentage error., , MCSE-004, , 4, , 1, , P.T.O.
Page 40 :
Download More:- https://www.ignouassignmentguru.com/papers, , (c), , Obtain the positive root of the equation, x2 - 1 = 0 by Newton-Raphson method,, , 8, , correct to two decimal places., , (d), , Explain the two pitfalls in the Gauss, , 4, , Elimination Method., (e), , Solve the following system of linear, equations using LU decomposition, , 6, , method :, 6x1 — 2x2 = 14, 9x1 — x2 + x3 = 21, 3x1 + 7x2 + 5x3 = 9., What is the lowest degree polynomial, , (f), , which satisfies the following set of values,, using forward difference polynomial ? Also, 6, , find the polynomial., x, , 0, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , f(x), , 0, , 7, , 26, , 63, , 124, , 215, , 342, , 511, , (g), , Calculate the value of the integral, , 1., , 5.2, ., , log x dx by Trapezoidal Rule., , 4, , Assume h = 0.2., Compare the numerical solution with the, exact solution., MCSE-004, , 2
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Download More:- https://www.ignouassignmentguru.com/papers, , (a) What do you mean by the terms "Accuracy", , 2., , and "Precision" ? How are they related to, , 4, , significant digits ?, (b), , Show that the equation x 3 — 6x — 1 = 0 has, a root in the interval I — 1, 0[. Obtain this, root using Successive Iteration or Bisection, , 8, , method., (c), , interpolating, Lagrange, the, Find, polynomial of degree 2 approximating the, function y = in x defined by the following, values mentioned in the table. Hence, , 8, , determine the value of In 2-7., , 3., , x, , 2, , 2-5, , 3-0, , y = In x, , 0.69315, , 0.91629, , 1.09861, , (a) Solve the initial value problem, u' = — 2tu 2 , with u(0) = 1, h = 0.2 on the, interval [0, 1]. Use the fourth order, classical Runge-Kutta method., (b), , Solve the following system of equations, using Gauss elimination with partial, pivoting :, , 8, , 2x + y + z = 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16, (c), MCSE-004, , What is the utility of residual plots ? What, is the disadvantage of residual plots ?, 3, , 4, , P .T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a) If a bank receives on an average X = 6 bad, cheques per day, what is the probability, that it will receive 4 bad cheques on any, given day, where X denotes the average, arrival rate per day ?, (b) A hosiery mill wants to estimate how its, monthly costs are related to its monthly, output rate. For that the firm collects data, regarding its cost and output for a sample, of nine months as given by the following, table :, Output, (tons), 1, 2, 4, 8, 6, , 5, 8, 9, 7, , Production Cost, (thousands of dollars), 2, 3, 4, 7, 6, 5, 8, 8, 6, , (i), , Draw the scatter diagram for the data., , (ii), , Find the regression equation when, the monthly output is the dependent, variable (x) and monthly cost is the, independent variable (y)., , (iii) Use this regression line to predict the, firm's monthly cost if they decide to, produce 4 tons per month., MCSE-004, , 4, , 12
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Download More:- https://www.ignouassignmentguru.com/papers, , (c) An individual's IQ score has a N(100, 152), distribution. Find the probability that an, individual's IQ score is between 91 and, 121., 5., , (a) Evaluate the integral I =, , n/2, i sin x dx using, , 0', formulae., Gauss-Legendre, two-point, Compare with the exact solution and the, exact value is I = 1., (b), , 8, , The following values of the function fXx) for, the values of x are, ft1) = 4, f(2) = 5, f(7) = 5 and fK 8) = 4., , (c), , MCSE-004, , Find the value of f16) and also the value of, x in the interval [1, 8] for which f(x) is, maximum or minimum., , 8, , Round off the number 4.5126 to four, significant figures and find the relative, percentage error., , 4, , 5, , 13,000
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Download More:- https://www.ignouassignmentguru.com/papers, , I MCSE-004 I, , No. of Printed Pages : 5, , MCA (Revised), Term-End Examination, June, 2016, , -.5.4 6, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., , 1. (a), , 2., If x= — approximated as 3.14, find the, 7, absolute error, relative error and relative, percentage error., , 3, , (b) Solve the following system of equations by, Jacobi iteration method :, 8x - 3y + 2z = 20, 4x + 1 ly - z = 33, 6x + 3y + 12z = 35, (Perform three iterations), , MCSE-004, , 1, , P.T.O.
Page 45 :
Download More:- https://www.ignouassignmentguru.com/papers, , (c), , Find the real root of the equation x = e-x,, using Newton-Raphson method. List the, 4+2, cases where Newton's method fails., , (d), , Determine the polynomial in x that best, fits as approximation of y by using, Lagrange's interpolation, from the, following data :, , 6, , x, , 0, , 1, , 3, , 5, , 6, , 9, , Y = gx), , -18, , 0, , 0, , -248, , 0, , 13104, , Find the value of, , (e), , (f), , log10 x dx, taking 8, , sub-intervals, correct to four decimal, places, by Trapezoidal rule., , 6, , In the table below the values of y are, consecutive terms of a series of which the, number 21.6 is the 6th term. Find the first, and the tenth term of the series., , 8, , x, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , Y, , 2.7, , 6.4, , 12.5, , 21.6, , 34.3, , 51.2, , 72.9, , (g), , Evaluate the integral, , 4, is x2dx using, 1, , Weddle's rule with h = 0.5., MCSE-004, , 2, , 5
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Download More:- https://www.ignouassignmentguru.com/papers, , 2. (a) Find Newton's Backward Difference from, the interpolating polynomial for the, following data :, x, , 4, , 6, , 8, , 10, , f(x), , 19, , 40, , 79, , 142, , Hence using the polynomial interpolate, f(9)., , 6, , 1, , Evaluate, , (b), , dx, using, 1+x, , 0, (i) Composite Trapezoidal rule,, (ii) Composite Simpson rule with 2 and 4, subintervals., (c) The table below gives the value of tan x for, 0.10 x 0.30 :, x, , 0-10, , 0-15, , 0.20, , 0.25, , 8, , 0.30, , y = tan x 0.1003 0.1511 0.2027 0.2553 0.3093, Find (i) tan 0.12, and (ii) tan 0-26., , 6, , 3. (a) A problem in statistics is given to the three, students A, B and C, whose chances of, 3, 1, solving it are 2— — and — respectively., 4, 1,4, What is the probability that the problem, will be solved ?, , 6, , MCSE-004, , 3, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (b), , A farmer buys a quantity of cabbage seeds, from a company that claims that, approximately 90% of the seeds will, germinate, if planted properly. If four seeds, are planted, what is the probability that, exactly two will germinate ?, , (c), , Calculate the correlation coefficient for the, following heights (in inches) of fathers (x), and their sons (y) :, x:, , 65, , 66, , 67, , 67, , 68, , 69, , 70, , y:, , 67, , 68, , 65, , 68, , 72, , 72, , 69, , (a) 1000 light bulbs with mean life of 120 days, are installed in a new factory and their, length of life is normally distributed with, the standard deviation of 20 days., (i) How many bulbs will expire in less, than 90 days ?, (ii) If it is decided to replace all the bulbs, together, what interval should be, allowed between replacements, if not, more than 10% should expire before, replacement ?, (b) In a partially destroyed laboratory, the, record of an analysis of correlation data,, the following results are legible :, Variance of X = 9, Regression equations :, 8X - 10Y + 66 = 0, 40X - 18Y - 214 = 0, , MCS E-004, , 8, , 4, , 8
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Download More:- https://www.ignouassignmentguru.com/papers, , 12, , Find :, (i) The mean values of X and Y, (ii) The correlation coefficient between, X and Y, (iii) Standard deviation of Y, 5., , ven —, (a)Given, y = y - x, where y(0) = 2., dx, Find y(0.1) and y(0.2), correct to four, decimal places, using Runge-Kutta Second, Order method., , 8, , Write the pitfalls in the Gauss elimination, method., , 2, , (b), (c), , MCSE-004, , Solve the initial value problem to compute, approximation for y(0.1) and y(0.2), using, Euler's method with h = 0.1,, dy, = 3e-4t, y(0) =1. Compare with, dt 2y, 5e-2t 3e-4t, exact solution y(t), 2, , 10, , 7,000
Page 49 :
Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004, , MCA (Revised), , 03015, , Term-End Examination, December, 2016, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., , 1., , (a) Let a = 0.345 x 10 0, b = 0.245 x 10-3 and, c = 0.432 x 10-3 . Using 3-digit decimal, arithmetic with rounding, prove that, 3, , (a + b) c a + (b + c)., (b), , Obtain the positive root of the equation, x 2 - 1 = 0 by Regula-Falsi method, correct, up to 2 decimal places., , (c), , Solve the following linear system of, equations using Gauss Elimination, method :, x1 + x2 + x3 = 3, 4x1 + 3x2 + 4x3 = 8, 9x 1 + 3x2 + 4x3 = 7, , MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , From the following data, estimate the, value of f(2.25) using Backward Difference, Formula :, X:, , 0, , 6, 0.5, , 1.0, , 1.5, , 2.0, , 2.5, , f(x) : 1.0 3.625 7.0 11.875 19 29125, (e), , Calculate the value of the integral, 5.2, , f, , log x dx using, , 4, , (i), , Trapezoidal rule,, , (ii), , 1, Simpson's — rule., 3, , Assume h = 0.2. Compare the numerical, solutions with the exact solution., (0, , 2x4+2=10, , Explain the concept of Exponential, Random Variable with a suitable example., , (g), , 5, , Find a polynomial of degree 2 with the, properties P(1) = 5, P(1.5) = — 3, P(3) = 0., , 4, , 2. (a) Given the following system of linear, equations, determine the value of each, variable using LU decomposition method :, 6x 1 — 2x2 = 14, 9x 1 — x2 + x3 = 21, 3x 1 + 7x 2 + 5x 3 = 9, MCSE-004, , 2, , 8
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Download More:- https://www.ignouassignmentguru.com/papers, , 6, , (b), , Evaluate, , [2 + sin (2 ,./i )] dx, , using, , J, 1, , 8, , Simpson's rule with 11 points., (c), , If a bank receives on an average X = 6 bad, cheques per day, what is the probability, that it receives 4 bad cheques on any given, , 4, , day ?, 2, , 3. (a) Evaluate the integral I =, , f, , 2x dx, , using, , 1 + x4, 1, the Gauss-Legendre 1-point, and 2-point, quadrature rules. Compare with the exact, solution., (b), , Calculate the correlation coefficient for the, following heights (in inches) of fathers (X), and their sons (Y) :, X:, , 65, , 66, , 67, , 67, , 68, , 69, , 70, , 72, , Y:, , 67, , 68, , 65, , 68, , 72, , 72, , 69, , 71, , (c) A box contains 6 red, 4 white and 5 black, balls. A person draws 4 balls from the box, at random. Find the probability that, among the balls drawn there is at least one, ball of each colour., MCSE-004, , 3, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a), , Solve the initial value problem, u' = – 2t u2 with u(0) = 1 and h = 0.2, on the interval [0, 11. Use the fourth order, 10, , classical Runge-Kutta method., (b) Estimate the missing term in the following, data which represents a polynomial of, , 4, , degree 3 :, x:, , 1, , 2, , 3, , 4, , 5, , f(x) :, , 3, , 7, , ?, , 21, , 31, , 6, , (c), , (x2, , Evaluate the integral, , + x + 2) dx, , 0, , using Trapezoidal rule, with h = FO., , 5., , 6, , (a) Three groups of children contain, respectively 3 girls and 1 boy, 2 girls and, 2 boys, and 1 girl and 3 boys. One child is, selected at random from each group. Show, that the chance that the three selected, 13, children consist of 1 girl and 2 boys is — ., 32, , MCSE-004, , 4, , 6
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , Find the most likely price in Bombay, corresponding to the price of, , 70 at, , Kolkata from the following data :, Kolkata Bombay, Average Price, , 65, , 67, , Standard Deviation, , 2.5, , 3.5, , Correlation coefficient between the prices, , 6, , of commodities in the two cities is 0-8., (c), , Fit a straight line to the following data, with x as the independent variable :, x, , 0, , 1, , 2, , 3, , 4, , Y, , 1.0, , 1.8, , 3.3, , 4.5, , 6.3, , Hence find the difference between the, actual value of y and the value of y, obtained from the fitted curve when x = 3., , MCSE-004, , 5, , 8, , 8,000
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Download More:- https://www.ignouassignmentguru.com/papers, , I MCSE-004 I, , No. of Printed Pages : 7, MCA (Revised), Term-End Examination, , 0E13 2 I, , June, 2017, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., , 1. (a), , Evaluate the relative error of the function, f = xy2z3 , if x = 37.1, y = 9.87, z = 6.052 and, Ax = 0.3, Ay = 0.11, Az = 0-016., , (b), , Use the Newton-Raphson method to find, the root of the equation x 3 — 2x — 5 = 0., , (c), , Using the data sin (0.1) = 0.09983 and, sin (0.2) = 0.19867, find the value of, sin (015) by Lagrange interpolation., Obtain the truncation error also., , MCSE-004, , 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d) A taxi hire firm has two taxies which it, hires out day by day. The number of, demands for a car on each day is, distributed as Poisson variate with, , mean, , 1.5. Calculate the proportion of the day on, which, , (e), , (i), , neither taxi is used, and, , (ii), , some demand is refused., , Determine the constants a and b by the, method of Least Squares such that y = ae bx, fitsheolwngda:, , Y, , MCSE-004, , 2, , 4-077, , 4, , 11.084, , 6, , 30.128, , 8, , 81.897, , 10, , 222.62, , 2
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Download More:- https://www.ignouassignmentguru.com/papers, , (0, , Find the root of the equation xe x = cos x, using the- Secant method, correct to four, decimal places. Do three iterations., , (g) Evaluate, , using composite, , 5, , Trapezoidal rule with n = 2 and 4., , 2. (a) Solve the initial value problem, dy = y – x with y(0) = 2 and h = 0.1, —, dx, using fourth order classical Runge-Kutta, method. Find y(0.1) and y(0.2), correct to, four decimal places., , MCSE-004, , 10, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (b) An automobile engineer is investigating, the effect of engine temperature on engine, oil consumption. The study results show, the following data :, , Temp (°C), , Consumption (%), , 100, , 45, , 110, , 51, , 120, , 54, , 130, , 61, , 140, , 66, , 150, , 70, , 160, , 74, , 170, , 78, , 180, , 85, , 190, , 89, , Determine, , the, , Goodness, , to, , fit, , parameter (R) and comment on whether the, predicted lines fit well into the data or not., MCSE-004, 4, , 10
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Download More:- https://www.ignouassignmentguru.com/papers, , . (a) Find the cubic polynomial using Newton's, forward interpolation formula, which takes, the following values : 7, f(X), 0, , 1, , 1, , 2, , 2, , 1, , 3, , 10, 0.6, , (b), , ei, 2, 1, e- dx, Use Simpson's 3- rule to find, 0, by taking seven ordinates., , (c), , Solve the following differential equation by, Euler's method :, dy y - x, , given y(0) = 1., —=, dx y + x, Find y approximately for x = 0.1 in five, steps., , MCSE-004, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a) Solve the following system of equations, using Gauss-Elimination method with, partial pivoting :, x1 + x2 + x3 = 6, 3x1 + 3x2 + 4x3 = 20, 2x1 + x2 + 3x3 = 13, (b), , Find an approximate root of the equation, sin x = 1 ; x E [1, 1.51 (x is measured in, radians). Carry out computations up to 3rd, stage, using Bisection method., , (c), , Form a backward difference table for, y = log x and determine the value of V3 y 40, from the table. The initial data to be used, for generating the backward difference, table is as follows :, , MCSE-004, , X, , Y, , 10, , 1-0000, , 20, , 1-3010, , 30, , 1.4771, , 40, , 1.6021, , 50, , 1.6990, 6, , 6
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Download More:- https://www.ignouassignmentguru.com/papers, , 5. (a) An irregular six-faced die is thrown and the, expectation that in 10 throws it will give five, even numbers is twice the expectation that it, will give four even numbers. How many, times in 10000 sets of 10 throws would you, expect it to give no even number ?, , (b), , Apply Gauss-Seidel iteration method to, solve the following system of equations :, 20x + y — 2z = 17, 3x + 20y — z = — 18, 2x — 3y + 20z = 25, 7, , Perform three iterations., , (c), , A real, , of the, , root, , equation, , f(x) = x3 — 5x + 1 = 0 lies in the interval, (0, 1). Perform three iterations using, Regula-Falsi method to obtain this root., , MCSE-004, , 7, , 3,500
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE 004, -, , MCA (Revised), Term-End Examination, , 07140, , December, 2017, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., 1. (a), , Evaluate the sum S = Nri + ,I6 + ,fd to 4, significant digits and find its absolute and, relative errors. 5, , (b), , Use Lagrange's Interpolation formula to, find the value of sin (n/6) given by y = sin x., , (c), , x, , 0, , 7E/4, , ir/2, , y = sin x, , 0, , 0.70711, , 1.0, , 5, , Determine the value of y when x =, Given that y(0) = 1 and y' = x2 + y. Use, Euler's method., , MCSE-004, , 5, 1, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , What are the pitfalls of Gauss Elimination, 5, , method ?, (e), , A2, Evaluate — (x 3 ) ., , (f), , An individual's IQ score has a Normal, Find the, , distribution N(100, 152)., , probability that the individual's IQ score is, 5, , between 91 and 121., (g), , Use Regula-Falsi method to find the roots, of the equation f(x) = x 3 + x – 1., , (h), , 5, , Calculate the value of the integral, 5.2, , i, , log x cbc by using, , 4, , (i), , Simpson's 1/3 rule,, 5, , (ii) Simpson's 3/8 rule., 2., , (a) Using the data given below, perform the, following tasks :, Subject A Subject B, , MCSE-004, , Mean Marks, , 36, , 85, , Standard, Deviation, , 11, , 8, , 2, , 10
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Download More:- https://www.ignouassignmentguru.com/papers, , Coefficient of correlation between A and, B = ±0.66., (i), , Determine the two equations of, regression., , (ii) Calculate the expected marks in A, corresponding to 75 marks obtained, in B., (b) Using the Runge-Kutta method, find y(0.2), y, for the equation dy, dx =, x • y(0) = 1., y+x, Take h = 0.2., , 10, , 3. (a) Solve the following system of equations by, using the Gauss Elimination method :, , 6, , x + 2y + z = 3, 2x + 3y + 3z = 10, 3x y + 2z = 13, (b) Solve the following system of equations by, using the LU decomposition method :, , 6, , x + y = 2; 2x + 3y = 5, , MCSE-004, , 3, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (c) Use the Jacobi method to solve the, following system of equations :, , 8, , 3x + 4y + 15z = 54.8, x + 12y + 3z = 39.66, 10x + y — 2z = 7.74, , 4., , (a) A thesis contains 100 misprints distributed, randomly throughout its 100 pages. What, is the probability that a page observed at, random contains at least two misprints ? 5, (b), , The tangent of the angle between the lines, of regression y on x and x on y is 0.6 and, 1, a=—, 2 ay . . Find r, , (c), , A polynomial passes through the points, (1, — 1), (2, — 1), (3, 1) and (4, 5). Find the, polynomial using Newton's forward, interpolation., , (d), , Find an approximate value of the root of, the equation x3 + x — 1 = 0, near x = 1,, using the Bisection method twice., , MCSE-004, , 4
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Download More:- https://www.ignouassignmentguru.com/papers, , 5., , (a) Discuss the formulas for the following :, (i), , 6, , Binomial distribution, , (ii) Poisson distribution, (iii) Normal distribution, (b), , If a bank receives on an average A = 6 bad, cheques per day, what is the probability, that it will receive 4 bad cheques on any, given day ?, , (c), , 6, , Given the values, x, , f(x), , 5, , 150, , 7, , 392, , 11, , 1452, , 13, , 2366, , 17, , 5202, , Evaluate f(9) using, (i), , Lagrange's formula, and, , (ii) Newton's divided difference formula., , MCSE-004, , 5, , 7,000
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Download More:- https://www.ignouassignmentguru.com/papers, , I MCSE-004 I, , No. of Printed Pages : 5, , MCA (Revised), Term-End Examination, Ft 7-, , I- r-, , June, 2018, , MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., , 1. (a), , Define relative and percentage error. Find, the relative and percentage error when the, value of it =, , (b), , 2, L, 7, , is approximated to 3.14., , 4, , Find the value of 'e', correct to 3 decimal, places., , 4, , 1, 1, 1, e= 1+ —+ —+ — +, , 2!, , (c), , MCSE-004, , 3!, , 4!, , Use the Newton-Raphson method to find, the root of the equation x3 - 2x – 5 = 0., Perform two iterations. Use initial, approximation xo = 2., 1, , 4, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , Solve the following system of linear, equations using the Gauss Elimination, method :, , 6, , x1 + x2 + x3 = 3, 4x1 + 3x2 + 4x3 = 8, 9x1 + 3x2 + 4x3 = 7, , (e), , Obtain the forward difference interpolating, polynomial from the following set of nodes :, x, , f(x), , 0, , 0, , 1, 2, , 26, , 3, , 63, , 4, , 124, , 5, , 215, , 6, , 342, , 7, , 511, 1, , (0, , Evaluate the integral, , if, , dx, 1+x, , 0, 1, Simpson's 8—3 th rule with h = — ., 3, MCSE-004, , 2, , using, , 6
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Download More:- https://www.ignouassignmentguru.com/papers, , (g), , A-farmer buys a quantity of cabbage seeds, from a company that claims that, approximately 90% of the seeds will, germinate if planted properly. If four seeds, are planted, what is the probability that, 'exactly two will germinate ?, , 6, , The tangent of the angle between the lines, of regression of y on x and x on y is 0.6 and, 1, a = - aY. Find a xr, 2 Y., (a) Solve the following system of equations by, using LU Decomposition method :, (h), , 2., , x+y= 2, 2x + 3y = 5, (b), , (c), , interpolating, Lagrange, the, Find, polynomial that fits the following data :, x, , 0, , 1, , 2, , 5, , f(x), , 2, , 3, , 12, , 147, , 7, , Calculate the value of the integral, 5.2, , f, , log x dx using Weddle's rule., , 4, , 3. (a) Show that the moment generating function, of a random variable X which is chi-square, distributed with v degrees of freedom is, M(t) = (1- 20- v/2., MCSE-004, , 3, , 5, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (b) In a partially destroyed laboratory record, of an analysis of correlation data, the, following results are legible :, Variance of X = 9, Regression equations, 8x - lOy + 66 = 0, 40x - 18y - 214 = 0, , (c), , 4., , Find, (i) the mean values of x and y,, (ii) the correlation coefficient between x, and y, and, (iii) the standard deviation of y., , 12, , What is the utility of residual plots ? Also, give one disadvantage of residual plots., , 3, , (a) Apply the fourth order Runge-Kutta, method to the following differential, equation :, dy _ 2xy2, dx y(0) =1, Obtain y(0.2), taking h = 0-2., , (b) Find the probability that an individual's, IQ score is between 91 and 121., Provided : the individual IQ score has, normal distribution with mean 100 and, variance 225., MCSE-004, 4, , 6, , 6
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Download More:- https://www.ignouassignmentguru.com/papers, , (c) Write short notes on any two of the, 4+4=8, following :, (i), , Goodness of Fit, , (ii) Newton-Cotes Formula, (iii) Non-linear Regression, 5., , (a) Solve by Jacobi's method, the following, system of linear equations :, , 7, , 2x1 – x2 + x3 = – 1, x1, , + 2x2 – x3 = 6, , x1 - x2 + 2x3 = - 3, , (b), , Suppose that the amount of time one, spends in a bank to withdraw cash from an, evening, counter, is, exponentially, distributed with mean 10 minutes, that is,, 1, X = — . What is the probability that the, 10, customer will spend more than 15 minutes, at the counter ?, , (c), , What do you mean by pseudo-random, number generation ? What is the practical, advantage of the concept of random, number generation ?, , MCSE-004, , 6,000
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , I MCSE-004 I, , MCA (Revised), Term-End Examination, December, 2018, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Maximum Marks : 100, , Time : 3 hours, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., 1., , (a), , Describe the term 'Error'. How are errors, generated in the calculation performed by, computers ?, , (b), , Show that a(b — c) ab — ac,, where a = 0.555 x 10', b = 0.4545 x 10', c = 0.4535 x 10'., and, Use 4-digit precision floating point and, significant digit rounding off., , 5, , Obtain the positive root of the equation, x2 - 1 = 0 by Regula Falsi method., , 6, , (c), (d), , Use Gauss elimination to solve, 10x1 — 7x2 = 7, — 3x1 + 2.099x2 + 6x3 = 3.901, 63E1 — x2 +, , MCSE-004, , 63E3 = 6., 1, , 6, P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (e), , (f), , Given f(x) = sin x, f(0.1) = 0.09983 and, fi0.2) = 0.19867, use the method of linear, interpolation to find fi0-16)., , 6, , Evaluate the integral, 6, , f, , (x 2, , +x+ 2)dx, , 0, , using Trapezoidal rule, with h = FO., , 6, , In turning out certain toys in the, manufacturing process in a factory, the, average number of defectives is 10%. What, is the probability of getting exactly, 3 defectives in a sample of 10 toys chosen, at, random,, by using Poisson, approximation ? (Take e = 2-72)., , 6, , (a) The population of a town in the census was, as given below. Estimate the population for, the year 1895., , 8, , (g), , 2., , Year : x, 1891, 1901, 1911, 1921, 1931, MCSE-004, , Population : y, (in thousands), 46, 66, 81, 93, 101, 2
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , Solve the equations, 2x + 3y + z = 9, x+ 2y+ 3z= 6, 3x + y + 2z = 8, by LU decomposition method., , (c), , Write two pitfalls of Gauss elimination, method., , 3. (a) Write short notes on any four of the, following :, 4x2=8, (i) Discrete Random Variable, (ii) Continuous Random Variable, (iii) Binomial Distribution, (iv) Poisson Distribution, (v) CM-square Distribution, (b), , From the following results, obtain the two, regression equations and estimate the yield, of crops when the rainfall is 22 cm and the, rainfall when the yield is 600 kg :, y (yield in kg), , x (rainfall in cm), , Mean, , 508.4, , 26.7, , S.D., , 36.8, , 4.6, , Coefficient of correlation between yield and, rainfall = 0-52., (c), , 8, , Write short note on Acceptance Rejection, method of random number generation., 4, MCSE-004, 3, P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a) Use Runge-Kutta method to solve the IVP,, y' = (t — y)/2 on [0, 0, 2] with y(0) = 1., Compare the solutions when h = 0.2 and, 0.1 respectively., (b), , Evaluate the integral, , using Gauss-Legendre three-point formula., Calculate the value of the integral, , (c), , 5-2, , log x dx, 4, , by Weddle's rule., 5., , (a), , The length of metallic strips produced by a, machine has mean 100 cm and variance, 2.25 cm. Only strips with weight between, 98 cm and 103 cm are acceptable. What, proportion of strips will be acceptable ? You, may assume that the length of a strip has a, normal distribution., , MCSE-004, , 4, , 8
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Download More:- https://www.ignouassignmentguru.com/papers, , (b) Fit a straight line to the following data, regarding x as the independent variable,, using least square approximation., x, , 0, , y, , FO, , ' 1, 1.8, , 2, , 3, , 4, , 3.3 ., , 4.5, , 6.3, , Hence, find the difference between the, actual value of y and the value of y, obtained from the fitted curve when x = 3., (c), , Estimate the missing term in the following, 6, , data using forward difference :, , fix), , MCSE-004, , 8, , 1, , 2, , 3, , 4, , 3, , 7, , ?, , 21, , 5, , 31, , 8,000
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 5, , MCSE-004 I, , MCA (Revised), Term-End Examination, 2019 0, MCSE-004 : NUMERICAL AND, STATISTICAL COMPUTING, Time : 3 Hours], , Maximum Marks : 100, , Note : Question No. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is allowed., , 1., , (a), , Find the roots of the equation cos x — 2x + 3 = 0 ,, correct to three decimal places., , (b), , [5], , Solve the following system of equations by using, Gauss-Elimination method :, , [5], , 2x1 + x2 + x3 = 10, + 2x2 + 3x3 = 18, x t + 4x 2 + 9x = 16, (c), , Determine the value of log 10 301, by using, lagrange interpolation on the tabulated data given, below :, , MCSE-004, , [5], ( 1 ), , [P.T.O.]
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Download More:- https://www.ignouassignmentguru.com/papers, , X, , 300, , 304, , 305, , 307, , log, oX 2.4771 2.4829 2.4843 2.4871, (d), , What is the probability of getting at least seven, heads, when ten coins are thrown, simultaneously "?, , (e), , [5], , What is "Goodness to fit test" ? Briefly discuss, the utility of "Goodness to fit test"., , [5], , 5.2, , (f), , Evaluate flog ydy by using Sinnpsons 3/8 rule., 4, , [5], (g)., , Given, the IQ score of individuals, has Normal, distribution N(100, 152 ). Determine the probability, that an individual's IQ score is between 91 and, , (h), , 2., , (a), , 121., , [5], , Briefly discuss the following :, , [5], , (i), , Non Linear Regression, , (ii), , Acceptance Rejection method, , Use Newton-Raphson method to find a root of, the equation x3-2x-5=0, , MCSE-004, , (2), , [5]
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , The tangent of the angle between the lines of, 1, , ., , regression y on x and x on y is 0.6, and a., =, , [10], , Find r.y ., dx, , (c), , Evaluate, , $1+x using Composite' Trapezoidal, , (.1, , rule with n=2 and 4., (d), , [5], , A polynomial passes through the following set of, points :, , [5], 1, , 2, , 4, , Find the polynomial using Newton's Forward, Interpolation., 3., , (a), , Solve the following system of linear equation by, Jacobi's Method :, 2x - y + z = -1, x + 2y - z = 6, x- y + 2z = -3, , MCSE-004, , ( 3), , [7]
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , What are the pitfalls of Gauss-Elimination, method ?, , (c), , [3], , Use Runge Kutta method to solve the inital value, problem y' = (t - y) / 2 on [0, 0.2] with y(0) = 1., Compare the solution with h = 0.2 and h = 0.1., [10], , 4., , (a), , Solve the following system of equations by using, LU decomposition method :, , [5], , x + y = 2 ; 2x + 3y = 5, (b), , Find an approximate value of the root of the, equation x3 + x - 1 = 0, near x = 1. Using Regula, Falsi method, twice., , (c), , [5], , Determine the Goodness to fit parmeter 'R' for, the data given below :, , [10], , x 100 110 120 130 140 150 160 170 180 190, y 45, , 51, , 54, , 61, , 66, , 70, , 74, , 78, , 85, , 89, , Analyse the results and comment on whether the, predicted lines fits well into the data or not., , MCSE-004, , (4)
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Download More:- https://www.ignouassignmentguru.com/papers, , 5., , (a), , In a partially destroyed laboratory record of an, analysis of correlation data, the following data are, only legible :, (i), , Variance of x = 9, , (ii), , Regression equation :, , [10], , 8x - lOy + 66 = 0, 40x - 18y - 214 = 0, Using the legible data given above, determine the, following :, Mean value of x and y, , (b), , (ii), , Correlation Coefficient between x and y, , (iii), , Standard deviation of y, , What do you mean by the term "Accuracy" and, "Precision" ? How are they related to the, significant digits 7, , (c), , What are residual plots ? Discuss the utility and, disadvantage of residual plots., , MCSE-004, , [5], , [5], , 5000
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Download More:- https://www.ignouassignmentguru.com/papers, , 58 4, MCSE-004, , No. of Printed Pages : 6, MCA (Revised), , Term End Examination, 2019, -, , MCSE-004 : NUMERICAL AND STATISTICAL COMPUTING, , Maximum Marks : 100, , Time : 3 Hours, , Note : Question No. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is allowed., 1., , (a), , If 0.333 is the approximate value of (1/3), find, absolute, relative and percentage error., , (b), , [3], , Determine the number of iterations required, to, obtain the smallest positive root of x3 - 2x -5 = 0., correct upto two decimal places, when Bisection, method is used., , (c), , [5], , Solve the following system of equations using, Gauss Elimination method :, , [5], , x+ 2y+ z = 3, 2x + 3y + 3z = 10, 3x - y + 2z - 13, MCSE-004/6000, (, , . ) 1111111111111111111111111111.111, , 1
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , Write probability distribution formula for Binomial, distribution and Poisson distribution., , (e), , [2], , Determine the value of f(x) at x=4, using Lagrange, Interpolation formula on the data given below : [5], x, f(x), , 1.5, 2.5, , 3, 2, 0.6, , x, , I e Calcutehvof, , (f), , 6, 20, , cbc , correct to five, , 0, , significant figures; by using Simpson's (1/3) rule., (Take n=6). [ 5], (g), , If a bank receives on an average A. = 6 bad, cheques per day. What is the probability that it, will receive 4 bad cheques on any given day? [5], , (h) Following data is given for marks in subjectA and, B of certain examination :, , Mean Marks, Standard Deviation, , [7], , Subject A Subject B, 36, 85, 11, 8, , Given, the coefficient of correlation between A and, B = + 0.66 ., MCSE-004/6000, , (2)
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Download More:- https://www.ignouassignmentguru.com/papers, , (I), , Determine the two equations of, regression., , (ii), , Calculate the expected marks in A,, corresponding to 75 marks obtained in B., , (i), , For, , x = 0.5555 El ;, , z = 0.4535 El ,, , y =- 0.4545 El, , and, , prove that x(y — z) # xy — xz, [3], , 2., , (a), , Solve the Quadratic equation 4x 2 + 8x — 21= 0, using two decimal digit arithmetic with rounding,, using any two of the following methods : [10], Bisection method, , (b), , (ii), , Secant method, , (iii), , Regula Falsi method, , Solve the initial value problem u' = —2tu 2 , with, u(0) =1, h = 0,2 on the interval [0,1]. Use the, fourth order classical Runge-Kutta method. [10], , 3., , (a), , Obtain the positive root of the equation x 2 - 1 = 0, by Newton-Raphson method, correct to two, decimal places., , MCSE-004/6000, , ( 3), , [8], [P.T.O.]
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Download More:- https://www.ignouassignmentguru.com/papers, , Solve the following system using LU, , (b), , decomposition method :, , (c), , 6x1 —, , 2x2, , =, , 9x1 —, , x2 +, , x3, , 3x1 +, , 7x2 +, , 5x3 =, , [7], , 14, , = 21, 9, , Determine the lowest degree polynomial, which, satisfies the following set of values, using forward, difference. Also find the polynomial :, , x, f(x), , 0, 0, , 1, 7, , 2, 26, , 3, 63, , 4, 124, , 5, 215, , 6, 342, , [5], 7, 511, , 5.2, , 4., , Calculate the value of the Integral, , (a), , flog x dx by, 4, , using Simpson's (1/3) rule and Simpson's (3/8), rule., (b), , [10], , Compute the value of R and R 2 for the data given, below, where R = S I jS. r S„ ., , S',, , 12, 0.96, 138, 138, , &'2, , 0, , Sample Size (i), x,, Y,, , MCSE-004/6000, , (4), , 21, 1.28, 160, , 15, 1.65, 178, , [5], , 1, 1.84, 190, , 24, 2.35, 210
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Download More:- https://www.ignouassignmentguru.com/papers, , Regression equation j) ; = 90 + 50x1 is used to, fill the table where e = y i — jii ., (c), , Solve the following system of equations by using, Jacobi Method, determine the results for two, approximations :, , [5], , 3x + 4y + 15z = 54.8, x + 12y+ 3z =, , 10x+, 5., , (a), , 39.66, , y — 2z = 7.74, , Write Short notes on the following :, , [6], , Binomial Distribution, , (b), , (ii), , Poisson Distribution ,, , (iii), , Normal Distribution, , Three bags of same type have the following, [6], , balls :, Bag 1 : 2 Black and 1 White, Bag 2 : 1 Black and 2 White, Bag 3 : 2 Black and 2 White, MCSE-004/6000, , (, , 5, , ), , [P.T.O.]
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Download More:- https://www.ignouassignmentguru.com/papers, , One of the bag is selected and one ball is drawn., It turns out to be white. What is the probability of, drawing a white ball again :, When the first one is returned/replaced., (ii), , When the first one is not returned/, replaced., , (c), , Calculate the correlation coefficient for the, following data :, , x, y, , :, :, , 65, 67, , 66, 68, , 67, 65, , [8], 67, 68, , 68, 72, , 69, 72, , 70, 69, , 72, 71, , Obtain the equations of lines of regression. Also, estimate the value of x for y = 70., x, , • MCSE-004/6000, , (6)
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Download More:- https://www.ignouassignmentguru.com/papers, , MCSE-004, , No. of Printed Pages : 7, , MASTER OF COMPUTER, APPLICATIONS (MCA) (REVISED), Term-End Examination, June, 2020, MCSE-004 : NUMERICAL AND, STATISTICAL COMPUTING, Maximum Marks : 100, , Time : 3 Hours, , Note : Question No. 1 is compulsory. Attempt any, three questions from the rest. Use of, calculator is allowed., 1. (a) Evaluate the sum :, , 5, , S = + ±, to four significant digits and determine, absolute and relative errors., (b) Use Newton-Raphson method to determine, 5, the root of the equation :, X3 — 2X — 5 = 0, Perform two iterations., , P. T. 0.
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Download More:- https://www.ignouassignmentguru.com/papers, , [2], , MCSE-004, , (c) Use Lagrange's interpolation formula to, find the value of sin (-7r, 6, , ,, , given y= sin x : 5, , x, , y = sin x, , 0, , 0, , It, , 0.70711, , 4, It, , 1.0, , 2, , (d) Evaluate the integral :, , 5, , dx, 01+x, by using trapezoidal rule with n = 2 and 4., (e) Use Secant method to find the root of the, equation :, , 5, , f(x) = —, e x + 5x + 2, 2, , Perform two iterations., (f), , A car rental firm has two cars which it, rents out day by day. The number of, demands for a car on each day is
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Download More:- https://www.ignouassignmentguru.com/papers, , MCSE-004, , 31, , distributed as Poisson variate with mean, 1.5. Calculate the proportion of days on, which, (i), , :, , 5, , neither car is used., , (ii) some demand is refused., (g) An irregular six-faced the is thrown, 10 times and the expectation of getting five, even numbers is twice of the expectation, that it will give four even numbers. How, many times in 10000 sets of 10 throws, would you expect it to give no even, number ?, , 5, , (h) What are the two pitfalls of GaussElimination method ? Give suitable, example for each., , 5, , P. T. 0.
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Download More:- https://www.ignouassignmentguru.com/papers, , [4], , MCSE-004, , 2. (a) The tangent of the angle between the lines, of regression y on x and x on y is 0.6 and, 1, ax= — a . Find rte,., 2, (b) Evaluate the integral :, , 8, , = 12 sin x dx, Jo, using Gauss-Legendre formula. Compare, the results with exact solutions obtained, by Simpson's rule. The exact value of I = 1., (c) Solve the system of linear equations, by, using Jacobi's method. Perform two, iterations :, , 7, , 2; — x2 + x3 = —1, xl + 2x2 — x3 = 6, xl - X2 + 2x3 = —3, , 3. (a) Solve the initial value problem if = —2tu2, , h = 0.2 on the intervalwithu(0)=1and, [0, 1]. Use the fourth order classical RungeKutta method. 10
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Download More:- https://www.ignouassignmentguru.com/papers, , [, , 5], , MCSE-004, , (b) Calculate the correlation coefficient for the, 10, following data :, •, , X, , Y, , 65, , 67 ., , 66, , 68, , 67, , 65, , 67, , 68, 72, , 68, 69, , 72, , 70, 72, , 69, 71, , Obtain the equations of lines of regression., Also estimate the value of X for Y = 70., 4. (a) Compute R and R 2 for the data given, 7, below :, Sample, , (i), , 12, , 21, , 15, , zi, , 0.96, , 1.28, , 1.65, , 1.84 2.35, , yi, , 138, , 160, , 178, , 190, , 138, , —, , size, , ei, , 1, , 24, , 210, , 0, , P. T. 0.
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Download More:- https://www.ignouassignmentguru.com/papers, , MCSE-004, , [6], , Regression equation j, = 90 + 50x is used, to fill the table, where, , e, = y —, , (b) Solve the following system of equations by, using LU decomposition method :, x+y=2, 2x + 3y = 5, (c) Write short notes on the following :, (i), , 6, , Binomial Distribution, , (ii) Poisson Distribution, (iii) Normal Distribution, 5. (a) What is error ? How are errors generated, in computers ? Briefly discuss the sources, of, , error., , (b) Evaluate the integral, Weddle's rule, with h = 0.5., , .1": x2 dx, , 5, using, 5
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Download More:- https://www.ignouassignmentguru.com/papers, , No. of Printed Pages : 6, , MCSE-004, , MCA (Revised), Term-End Examination, February, 2021, MCSE-004 : NUMERICAL AND STATISTICAL, COMPUTING, Time : 3 hours, , Maximum Marks : 100, , Note : Question no. 1 is compulsory. Attempt any three, questions from the rest. Use of calculator is, allowed., , 1., , (a), , What is precision ? How does precision, differ, , from, , accuracy, , ?, , Give, , suitable, , example in support of your answer., (b), , 5, , Estimate the missing term in the following, data, using forward differences :, , 5, , x, , 1, , 2, , 3, , 4, , 5, , f(x), , 3, , 7, , ?, , 21, , 31, , 4, , (c), , Evaluate the integral I =, , , , x 2 dx , using, , 1, , Simpson’s, MCSE-004, , 1, rule with h = 0·5., 3, , 1, , 5, P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (d), , If a bank receives on an average = 6 bad, cheques per day, what is the probability, that it will receive 4 bad cheques on any, given day ? denotes the average arrival, rate per day., , (e), , Solve, , the, , 5, following, , system, , of, , linear, , equations using the Gauss Elimination, method :, , 5, , 2x + y + z = 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16, (f), , Determine the constants a and b by the, method of least squares such that y = a ebx, fits the following data :, , MCSE-004, , 5, , x, , y, , 2, , 4·077, , 4, , 11·084, , 6, , 30·128, , 8, , 81·897, , 10, , 222·62, , 2
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Download More:- https://www.ignouassignmentguru.com/papers, , (g), , (h), , Find, the, Lagrange’s, interpolating, polynomial of degree 2, approximating the, function y = ln x. Hence determine the, value of ln 2·7 where x = 2, 2·5, 3., , 5, , Explain Bisection method. Apply the, method to determine the roots of the, equation. Perform 3 iterations., , 5, , f(x) = 0·5, 2., , (a), , ex, , – 5x + 2, , What is ‘‘Goodness of fit test’’ ? What is the, utility of this test ? Consider the following, data and perform ‘‘Goodness of fit test’’ over, it :, x, , y, , 100, , 45, , 110, , 51, , 120, , 54, , 130, , 61, , 140, , 66, , 150, , 70, , 160, , 74, , 170, , 78, , 180, , 85, , 190, , 89, , Now comment, whether the data is fitted, well or not., MCSE-004, , 3, , 10, , P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , (b), , Use Runge-Kutta method to solve the, initial, , value, , problem, , y = (t – y)/2, , on, , [0, 0·2] with y(0) = 1. Compare the solution, when h = 0·2 and h = 0·1., 3., , (a), , 10, , Three bags of same type have the following, balls :, Bag 1 : 2 black 1 white, Bag 2 : 1 black 2 white, Bag 3 : 2 black 2 white, Randomly one bag is selected and one ball, is drawn. It turns out to be white. What is, the probability of drawing a white ball, again provided the first ball is not returned, to the bag ?, , (b), , 7, , What are residual plots ? What is the, utility of residual plots ?, , (c), , 5, , Show that the moment generating function, of a random variable X which is Chi-square, distributed with v degrees of freedom is, M(t) = (1 – 2t)–v/2, , MCSE-004, , 4, , 8
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Download More:- https://www.ignouassignmentguru.com/papers, , 4., , (a), , Find an approximate value of the root of, the equation x3 + x – 1 = 0, near x = 1., Using Regula-Falsi method, perform two, iterations., , (b), , 6, , Solve the system of equations by using, Gauss-Seidel iteration method, perform, two iterations. Use (0, 0, 0) as initial, approximation., , 7, , 8x – 3y + 2z = 20, 6x + 3y + 12z = 35, 4x + 11y – z = 33, (c), , The following data is given for marks in, subject A and B of a certain examination :, Subject A, , Subject B, , Mean Marks, , 36, , 85, , Standard, deviation, , 11, , 8, , Coefficient of correlation between A and, B = 0·66., (i), , Determine, , the, , two, , equations, , of, , regression., (ii), , Calculate the expected marks in A, corresponding to 75., , MCSE-004, , 5, , 7, P.T.O.
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Download More:- https://www.ignouassignmentguru.com/papers, , 5., , (a), , How does error measure accuracy ? Discuss, the different types of errors used to, determine the accuracy., , (b), , Calculate, , the, , value, , 5, of, , the, , integral, , 5·2, , I=, , , , log x dx, , using, , Weddle’s, , rule., , 4, , Use h = 0·6., (c), , 5, , Write short notes on any two of the, following :, , 10, , (i), , Chi-square distribution, , (ii), , Acceptance-Rejection method, , (iii) Newton-Cotes formula, , MCSE-004, , 6
