Question

PLEASE SOLVE ONLY QUESTION B

A. LetX1,X2, ..., Xn be identically and independently distributed random variables with each having zero mean and variance σ. If j is defined as z,-X -X, j -1,2,..n where 7t k-1 then find E(Z,) and Var Z)

B. Let be identically and independently distributed exponential random variables with each having probability density function $e^{-y}$ . Then, find the probability density function of

$V=Y_1 - \frac{1}{3}\sum_{j=1}^{3}Y_j$

HINT- Use the following decomposition:

$\frac{1}{(a-z)^2(b-z)} = \frac{1}{(a-b)^2}\frac{1}{b-z} - \frac{1}{(a-b)^2}\frac{1}{a-z} + \frac{1}{b-a}\frac{1}{(a-z)^2}$   

Answer 1