conditional distribution of X|X + Y is
A:-Uniform
B:-Geometric
C:-Binomial
D:-Hyper Geometric
Correct Answer:- Option-A

Question53:-Consider a random experiment with two possible outcomes success
and failure. Experiment is repeating n times independently. Let X denote the no. of
success with constant probability p. Distribution of the no. of failure is

A:-Poisson

B:-Multinomial
C:-Geometric

D:-Binomial

Correct Answer:- Option-D

Question54:-Which of the following statements is/are correct about Cauchy
distribution ?

i. For a Cauchy random variable, central moments exist

ii. For a Cauchy random variable, mean does not exist

iii. For a Cauchy random variable, characteristic function exists

A:-All of the above (i, ii and iii)
B:-Only (i and ii)

C:-Only (ii and iii)

D:-Only (i and iii)

Correct Answer:- Option-C

Question55:-Let X and Y are two independent exponential random variables with
parameters 2 and 3. Which of the following is correct ?

A:-X + Y ~ exponential (5)
B:-X + Y ~ Gamma (5, 2)
C:-Min(X, Y) ~ exponential (5)
D:-Max(X,Y) ~ Exponential (5)
Correct Answer:- Option-C

Question56:-Let x, , x... . xX, be a set of n independent observation taken from U(0,
2). Let Xu, Xm, ..., Xm be the ordered pair of sample observations. Then the joint
distribution of is Xo, Xa, ..., Xmis

A:-n!
8.
1”
0:-

Correct Answer:- Option-D