062/21

~ F(x)is a distribution function, then which of the following is not a distribution function ?

A) (00% 8) 1-1- 0(5

©) 1-3۴00 + (F(x))> ഉ) 1-[1- F(x]?
‏۔‎ The probability generating function of a random variable X is १.८) = प्र +भ 1151 , then the mean of Xis

0.9

A) 1 8) 1/9 C) 0.9 D) 9

‎Let the discrete random variables X and ۷ have the joint probability mass function‏ ۔
=> 2-
‎P[X =x, = ४] = ९ 3012‏
‎५४-८0, 1 2,‏ 1/1

‎which of the following is true ?

‎A) Marginal distribution of X is Poisson with mean 2
8) E(Y)=2

‎©) ‏لازم‎ =K] =(K +1) P[Y=K +1], K=0,1,2,...
D) PIX>0Y < 1( = 1- ‏2ج‎

‎VX follows‏ < ۷ء0 <م ,0 حر ,61 = ‎Let X be a random variable having the 0.6.1. f(x)‏ ۔

‎A) Normal B) Gamma C) Weibull D) Beta

‎~ A telephone operator on an average handles 4 calls every 2 minutes. What is the probability that
there will be no calls in the next minute ?
1

‎A) 2 8) = ‏کو رہ‎ ഉ) 60
e
~ Let ‏رولا‎ Xp, - - - , X, be independent and identically distributed random variables following (10, 1]
distribution. Let ×0 denote the first order statistic. Then the mean of ×0 is given by
1 2
ಬ ವದ್ಯ 8) ೧೬1 ௦) D) (n +1)
n+1 (n+ 12

‎. Let X and ‏لا‎ 06 two independent standard normal variates. Let W = - X and Z = - ‏,لا‎ then which of
the following pairs is not distributed as bivariate normal distribution ?
A) )۷( 8) 062) ©) ൧൬ D) (x, W)

‎. Let ‏رركا‎ Xo, - - - , X, be a random sample from Ny (ಓ >) population. To test Hp : |! =p against Hy : ‏1ز‎ Ug,
the correct relationship between the likelihood ratio test statistic A and Hotelling’s T? statistic is

‎x
‎A) ‏لحر‎ B) neh
n-14+T n-14+T
2 2
©) ചടി ‏رم‎ പ
n-1 n-1

‎. Let X and Y be two chisquare random variables with respective degrees of freedom n and m. Then
which of the following is always true ?

‎A) ೫ +۷ follows chisquare distribution with m +n degrees of freedom

‎B) mz follows an F distribution with (n, m) degrees of freedom
n

‎©) E(X+Y)=me#n