Homework Answers

The joint probability density function of two random variables X1 and X2 is given by f(x1, x2) = { 8,        0 < x1 < x2 < 1
             0,           elsewhere
 Let S = X1/x2  and V = x2 , using the change of variable technique find the joint probability density function of S and V

You are asked to find the mean and variance of a random variable Y whose distribution has probability generating function is

qr /1 − (1 − q)r. 0 < q < 1 

 Let S be a subset of F3 defined as S = {(x, y, z) € F3 = x +y + 2x – 1=0}. Then determine S is a subspace of F3 or not.

 Suppose that X and Y have bivariate normal distribution with the probability density function f(x1, x2) = k exp − (8X^2 − 6XY − 18Y^2 ) Find (a) Pr(X + Y > 1/2) (b) the joint moment generating function of Z1 = 2X − XY and Z2 = 3X + 2Y

Let X,Y be a random sample from the distribution

f(x) = 1 0 < x < 1

Further let Y = max(X,Y). Using the distribution function technique,

find the probability density function of Y. Hence find its mean and variance values.

Let X1, X2 have joint probability density function

f(x1, x2) = {

1/8e

−(8x1+x2)

, x1,x2>0

0, elsewhere

Find the probability density function of Y =1/2 (X1 + X2).