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“choose the most correct alternative, " pelow for each question., , , , ae. THE correct relation between fourth cumulant and central moment is, , (a) Ke = Hs Ab Ky = py = 3;, (a) Ke = Ha + 3 (d) Ky = log jis, The second cumulant of a discrete r, Vv, X 18.1005..., (a) & (b) Wa, —_{e) both (@) and (b) (d) none of these, : __ IfX is symmetric random variable with E(x) = p then E[X - pf’ is ......, @) 3 (b) 1, (oy —~ 9 (d) -1, , A discrete random variables X has mean ‘a’, then the expression, , E[X-al? is......., (a) V(X) (b) 1, _(c}both (a) and (b) (d) neither (a) and (b), , __ If F,(x) is a cumulative distribution function of rv. X then ........... ~, , (a) OSF,X)S1, (b) F,(x) is defined for all values of X, , (c) F,(x) is non-decreasing, , (A) all of these, . Harmonic mean of continuous rv. is ......, , 1, (a) E(x) () Ea), , 5 wl)
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Bb. Tare Hh. VIG LP IUN, lobe) rd ———__—— —— ——Ohs ty, 7. If My(t) is m.g.f. of X then value of Mx(0) = «++ a, (a) 0 (b) - 1, ~ (ot (d) None of these, 8. If Mx(t) is the m.g.f. of continuous rv. X then Mc¢,{t) is .....,, (a) Mx(t) (b) C Mx(t), \_(--My(Ct) (d) Mx(t/C), 9. If Xis rv. then E(X - a) =..., L@Htm-a (b) E(x), () EX)+a . (d) a—-E(X), 10. If F(x) is distribution function of random variable X then F(- ) is n, (a) 1 \__—-¢by 0, (¢) -1 (d) - 0, , 11. Which of the following is a discrete rv. ?, (a) weight of an individual, (b) altitude of a certain place, (c) time required to complete the task, ( _Hdy size of a family, 12. Which of the following sample spaces is a discrete sample space?, , (a) {|x 20} (b) K] ~ © < x < oo}, , () &|-5sxs5} \ (D4 | x is positive integer}, 13. If F(x) is a distribution function and x, > Xi then ......, (a) F(X2) < F(x) (b) F(x.) < F(x), HO Fe) 2 Fa) (d) F(x.) s F(x.), 14. A continuous random variables X has mean M, then th i, EX = MP is sess © expression, (@) ps (b) ks, Le both (a) and (b) (d) none Of these, 15. If X is a discrete rv. then P(a < X < b)is......,, (a) Fa)-F(b) \fbY F(b) ~ Fray Pla), (c) 1 - F(a) + F(b) (d) f(b) - fay, 16. If Mx(t) is m.g.f. of rv. X then My— m(t) = 0..., \_ey eM x(t) (b) Mx(t) = erm, , () e™Mx(t) (d) Mx(t) - e™, , —
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ae telln, , erent nnn OFC Distributions taking o....., 7, suppose Y is @ symmetric random vari, , E(Y = M)? Fre able with E(Y) © m, Then, 2, )3 3, @) 3 (b) 5, {o}-0 (d) 1, 18. For any two r.vs. X and Y, [e (| © soosees, @ vO li, , (EM) (4), , 19, Moment generating function is affected by change of, , (a) origin (b) scale, (c)_origin and scale, , (d) neither origin nor scale, 20. If Mxi(t) is the m.g.f. of continuous r. v. X then M3x(t) is, , (a) 3Mx(t) —foy M,(3t), () e* Mx(t) (d) Mx(3/t), 21. If X is a discrete r.v. then E () iS..., (a) AM (b) HM, (c) GM \__(d)-none of these, 22. A discrete random variables X has mean 25, then the expression, E[X - 25)’ is......, (a) py (b) p12, (fy (d) none of these, 23. A cumulant generating function is affected by change of......, (a) origin (b) scale °, \_{e}origin and scale (d) neither origin nor scale, , 24. A random variable X has mean 10, then the expression E[X - 10}° is, , @ b) OO, (© both (a) and (b) (d) none of (a) and (b), , 25. A discrete rv. X has mean and variance 2 and 1 respectively, EQX? + 3X) is..., , \ 8-16 wl, , (c) 12 (d) none of these
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Objective Type Questions, , A Fill in the blanks and complete the statements (Q. 1 to 26):, 1. If Xis 3 Poisson (m) variate then its mean is and variance, , «<, , re :, Poisson distribution with parameter m is, , “The rth cumulant of Poisson distribution is, Poisson distribution with parameter m has P.G.F., , ' The cumulants of Poisson (m) distribution are .......... he, If X and Y are independent Poisson r.v.s, then X + Y follows, , , , , , oe eae, , en distribution., If X > Poisson (m), then P (x + 1) =... P(x)., , , , 7., , 8. If X > Poisson (m;) independent of Y > Poisson (mz), then,, (i) conditional distribution of X given X + Y = Nis ess, (ji) E(X)X+Y¥en) =u., (ii) Var XX +Y =n) = wa., (iv) E (YI WV sccicinins, , (v) Var (VIX + ¥ = n)-=, , Pe eeeeeeeees
