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STATISTICS, UNDER-GRADUATE SYLLABUS, B.A./B.Sc. Part I EFFECTIVE FROM 2014 EXAMINATIONS, Paper I: Probability Theory, Unit I: Random Experiment and Probability Measure, Random experiments, sample space, events, algebra of events, axiomatic definition of, probability, probability spaces, relationship of axiomatic and classical probability, role of, frequency ratios, properties of probability measure, subadditivity, Boole’s inequality,, probability of union of events, matching problem, repeated birthday problem, occupancy, problem, statistics of physical particles, conditional probability and associated probability, space, Bayes theorem, independence of events., Unit II: Random Variable and Random Vector, Random variables as functions, induced probability measure via inverse mapping, induced, probability distribution, distribution functions, distribution functions and their properties,, probability mass function (pmf) of discrete random variables, probability density function, (pdf) of continuous random variables,, Random vector, marginal and conditional distributions, independence of random variables, Unit III: Mathematical Expectation and Functions of Random Variables, Mathematical expectation, moments, factorial moments, moment generating function,, probability generating function, Expectation of jointly distributed random variables, marginal, and conditional expectation, correlation, Chebyshev’s inequality, Markov’s inequality,, functions of random variables., Unit IV: Statistical Distributions, Bernoulli distribution, binomial distribution, Poisson distribution, derivation of Poisson, distribution as a limiting case of binomial distribution, geometric distribution, negative, binomial distribution, hypergeometric distribution, multinomial distribution, uniform, distribution, normal distribution and its relationship with the binomial and Poisson, distribution, Cauchy distribution, bivariate normal distribution and its marginal and, conditional distributions., Book recommended:, 1. Beumont, G.P.: Probability and random variables., 2. Meyer, Paul L. (1970): Introductory probability and statistical applications, Addision, Wesley.

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3. Mukhopadhyay, P. (1996): Theory of Probability, New Central Book Agency, Calcutta., 4. Parzen, E. (1960): Probability theory and its applications, Wiley Eastern., Paper II: Statistical Methods and Computer applications, Unit I: Computer Applications, Origin of computers; Computer generations; Importance of computers; Hardware, components: CPU, Memory, Input output devices. Mouse-navigation tool. Operating, system: History, Windows operating system-Interface; File management; Input output, services., Software: Introduction to System software; Application software: Word processing software, – Microsoft Office Word 2007, Spread sheet software – Microsoft Office Excel 2007,, Presentation software – Microsoft Office PowerPoint 2007 (Interface of all the three, application software, File handling, Editing, Formatting, and final output), Excel as a database software: Cell referencing, Concept of list, Manipulation of data, Data, sorting and filtering, Naming of cells, Functions specifically Numeric/Mathematical, functions, Statistical functions, Logical functions, and Lookup functions; Statistical analysis, using Excel – Descriptive statistics, Curve fitting, Correlation, and Regression analysis; Excel, graphs., Basics of internet and its application in communication., R - Statistical package: Basics of R, R Studio and R commander; Creation of data files;, Import export of data files; Transformation of data; Graphical representation of data using, R; Descriptive statistics using R., Unit II: Visualization of data and descriptive statistics, Concept of Statistical population and sample, classification of data, quantitative and, qualitative data, ordinal and nominal data, time series and cross sectional data, multivariate, data., Construction of tables with one or more factors of classification, Diagrammatic and, graphical representation of grouped data. Frequency distributions, cumulative frequency, distributions and their graphical representation, histogram, frequency polygon and ogives,, Stem and leaf chart. Box plot, scatter plot for bivariate data, trellis plot for multi-variable, data., Measures of central tendency, dispersion, moments, skewness and kurtosis., , 2

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Unit III: Correlation and Regression for Bivariate Data, Simple linear regression, method of least squares, correlation coefficient, correlation ratio,, intraclass correlation, rank correlation, fitting of some nonlinear curves., Unit IV: Multivariate Data and analysis of categorical data, Multivariate data: Multiple regression, multiple and partial correlation for three variables., Analysis of Categorical Data: consistency, independence and association of attributes,, coefficient of contigency., Books recommended:, 1. Freund J.E (2001): Mathematical Statistics, Prentice Hall of India., 2. Goon, A.M., M.K. Gupta and B. Dasgupta (1991): Fundamentals of statistics, vol I,, World Press, Calcutta., 3. Goon, A.M., M.K. Gupta and B. Dasgupta (1991): Fundamentals of statistics, vol, II,, World Press, Calcutta., 4. Weatherburn C.E. (1961): A first course of Mathematical statistics, Cambridge University, press., 5. Sinha, P.K. (2010): Computer fundamentals, University Science press., 6. Rajaraman, V. (2010): Fundamentals of computers, PHI., 7. White, R. (1999): How computers work., Practical, Numerical problems and solutions based on theory papers I and II., , 3

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B.A./ B.Sc. Part II Effective from 2015 Examinations, Paper I: Statistical Inference, Unit I: Functions of Random Variables, Random sample from a given pdf or pmf, Functions of random variables and their, distributions., Unit II: Sampling Distributions, Sampling distribution of a statistic, Derivation of  2 , t, F and z distributions, Beta, Gamma, and Laplace densities, Binomial and Poisson indices of dispersion., Unit III: Estimation Theory, Sufficiency, factorization theorem, consistency and the background theory of WLLN,, Bernoulli theorem and CLT for iid variates Unbiasedness, Estimation method of maximum, likelihood, method of moments., Unit IV: Hypothesis Testing, Statistical Tests of Hypothesis- Fundamental concepts including the power function, p, values, Neyman and Pearson Lemma, most powerful (MP) and uniformly most powerful, (UMP) tests, Applications of  2 , t, F and z distributions in tests of significance, large sample, tests based on binomial and normal distributions., Books recommended:, 1. Hogg, R. V. and Craig, A. T. (2004): Introduction to Mathematical Statistics, Pearson, Edward (Indian Print)., 2. Rohatgi, V. K. and Saleh A. K. Md. E (2005). An Introduction to Probability and, Statistics, Wiley, New York., 3. Rohatgi, V.K. (1986): An introduction to probability theory and mathematical statistics,, Wiley Eastern., Paper II: Applied Statistical Analysis, Unit I: Simple random sampling and Stratified sampling, Sample surveys versus complete enumeration, Non sampling errors, Simple random, sampling with and without replacement, simple random sampling for attributes, Stratified, random sampling, advantages of stratification, methods of allocation., , 4

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Unit II: Use of auxiliary information, systematic and cluster sampling, Use of auxiliary information: Ratio, regression and product method of estimation, Systematic, sampling, Cluster sampling with equal clusters., Unit III: Quality Control, Importance of statistical methods in industrial research and practice, specification of items, and lot qualities corresponding to visual gauging, count and measurements, types of, inspection, determination of tolerance limits. General theory of control charts, causes of, variation in quality, control limits, sub-grouping, summary of out-of control criteria, charts, for attributes, np chart, p-chart, c- chart, Charts for variables- X- and R charts, design of X, and R charts versus p-charts, cumulative sum chart, V-mask., Principle of acceptance sampling- problem of lot acceptance, stipulation of good and bad, lots, producers and consumers risks, single and double sampling plans, their OC functions,, concepts of AQL, LTPD, AOQL, average amount of inspection and ASN function,, rectifying inspection plans., Unit IV: Vital Statistics, Crude, death rates, infant mortality rates, standardized death rate, complete and abridge life, table – construction and uses, mortality rate and probability of dying, use of survival tables., Measurement of fertility - crude birth rate, general fertility rate, total fertility rate, gross, reproduction rate, net reproduction rate, population growth and logistic model for, population projection., Books recommended:, 1. Agrawal, S.N. India’s population problem., 2. Cochran, W.G. (1977) Sampling Techniques, Third Edition, Wiley., 3. Goon, A.M., M.K. Gupta and B. Dasgupta (1996): Fundamentals of statistics, vol, II,, World Press, Calcutta., 4. Montgomery, D. C. (2003): Introduction to the statistical quality control. John Wiley &, Sons., 5. Mukhopadhyay, P. (1996): Inferential Problems in Survey Sampling. New Age, International., 6. Mukhopadhyay, P. (1999): Applied Statistics. New Central Book Agency Pvt. Ltd.,, Calcutta., 7. Mukhopadhyay, Parimal (1998): Theory and Methods of Survey Sampling. Prentice Hall., 5

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8. Rama Kumar, R. (1986): Technical Demography, Wiley Eastern Ltd., 9. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. and Asok, C. (1984): Sampling Theory of, Surveys with Applications, Iowa State University Press and Indian Society of Agricultural, Statistics., Paper III: Statistics Practical, Numerical problems and solutions based on theory papers I and II., , 6

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B.A./B.Sc. III Effective from 2016 Examinations, Paper I: Advanced Inference, Unit I: Truncated, Mixture and Non-central Distributions, Compound, truncated and mixture distributions, Non-central chi-square, t- and Fdistributions and their properties., Unit II: Estimation Theory, Completeness and sufficiency, Rao-Blackwell theorem, Lehman Scheffé theorem, one, parameter exponential family and its completeness, Cramér-Rao inequality, Best linear, unbiased estimator, Unit III: Testing of Hypothesis, Likelihood ratio test, Unbiased test, Neyman Pearson Lemma for randomized tests,, Randomized test for binomial and Poisson distributions,  2 -test of goodness of fit,, Contingency table, Test of equality of several variances, Significance test for correlation, coefficient., Unit IV: Bayesian Estimation and Interval Estimation, Prior and posterior distributions, Bayes estimators under squared error loss function,, posterior variance and Bayes risk., Interval Estimation: Concepts of Confidence Interval and Confidence Coefficient, Shortest, length confidence interval., Books recommended:, 1. Hogg, R. V. and Craig, A. T. (2004): Introduction to Mathematical Statistics, Pearson, Edward (Indian Print)., 2. Rohatgi, V. K. and Saleh A. K. Md. E (2001). An Introduction to Probability and, Statistics, Wiley, New York., 3. Rohatgi, V.K. (1986): An introduction to probability theory and mathematical statistics,, Wiley Eastern., Paper II: Design of Experiments and Nonparametric Statistics, Unit I: Analysis of Variance, One-way ANOVA, two-way ANOVA with single observation per cell and equal number of, observations per cell., , 7

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Unit II: Design of Experiments, Randomization, Replication, Local Control, Completely randomized design (CRD),, Randomized block design (RBD), Latin square design (LSD), Missing plot technique, 22 and, 23factorial experiments., Unit III: Order Statistics, Order statistics, Distribution of maximum, minimum and r-th order statistic, Joint, distribution of r-th and s-th order statistic, distribution of range, distribution free confidence, intervals for quantiles and distribution free tolerance intervals., Unit IV: Non parametric Tests, Sign test, Wilcoxon test, Median test, Run test., Books recommended:, 1. David Herbert A. and H. N. Nagaraja (2004): Order Statistics, Wiley Interscience (John, Wiley and Sons)., 2. Gibbons Dickinson, J. and Subhabrata Chakraborti (2003) Nonparametric Statistical, Inference, Fourth Edition, Marcel Dekker., 3. Goon, A.M., M.K. Gupta and B. Dasgupta (1991): Fundamentals of statistics, vol, II,, World Press, Calcutta., 4. Gupta, S.C. and V.K. Kapoor (2007): Fundamentals of Applied Statistics, Sultan Chand, and Sons., 5. Hoel, P.G. (2005): Introduction to mathematical statistics, John Wiley, 6. Mukhopadhyay, P. (1999): Applied Statistics. New Central Book Agency Pvt. Ltd.,, Calcutta., 7. Sidney Siegel: Nonparametric statistics for the behavioral sciences., Paper III: Economic Statistics and Operations Research, Unit I: Economic Time series and Income Distributions, Time Series, Components of time series, additive and multiplicative models, methods of, determination of trend, growth curves, analysis of seasonal component and seasonal indices., Analysis of income and allied distributions - Pareto distribution, graphical test, fitting of, Pareto’s law, illustrations, log-normal distribution and its properties, Lorenz curve, Gini’s, coefficient., , 8

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Unit II: Index Number and Demand Analysis, Index number: Price relatives and quantity or volume relatives. Link and chain relatives,, computation of index numbers, Laspeyre’s, Paasche’s, Marshal - Edgeworth’s and Fisher’s, index numbers, chain base index number, consumer price-index numbers. Tests for index, numbers: Time and Factor reversal tests., Theory and analysis of consumer’s demand: Law of demand, Price elasticity of demand,, Estimation of demand curves; Forms of demand functions, Engel’s curves, Income elasticity, of demand., Unit III: Linear Programming, Elementary theory of convex sets, definition of general linear programming problems (LPP),, formulation problems of LPP, examples of LPP, graphical and Simplex method of solving, an LPP, artificial variables, duality of LPP, Transportation Problem (non-degenerate and, balanced cases only), Assignment Problem, solution of sequencing problems, Simulation and, network scheduling by PERT/CPM., Unit IV: Game Theory, Game theory: Two person two-choice zero-sum games, Strictly determined 2×2 game, pure, strategies, 2×2 non strictly determined game and mixed strategies, Values and its uniqueness,, Fundamental theorem for 2×2 games, Solution of games using linear programming method, and algebraic method., Books recommended:, 1. Goon, A.M., M.K. Gupta and B. Dasgupta (1991): Fundamentals of statistics, vol, II,, World Press, Calcutta., 2. Hiller, F. S. and Libermann, G. J. (1995). Introduction to Operations Research,, McGraw Hill., 3. Mckinsey, J.C.C. (1952). Introduction to the Theory of Games, McGraw Hill Book, Co., 4. Mukhopadhyay, P. (1999): Applied Statistics. New Central Book Agency Pvt. Ltd.,, Calcutta., 5. Sharma, J.K. (1997). Operations Research: Theory and Applications, MacMillan, India Limited., 6. Swaroop, K., Gupta, P.K. and Singh, M.M. (1985). Operations Research, Sultan, Chand & Sons., 9

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7. Taha, H.A. (1982). Operations Research: An Introduction, Macmillan Publishing, Company., Paper IV: Statistics Practical, Numerical problems and solutions based on theory papers I, II and III., , 10