1. Let Y be a continuous random variable with PDF ()=^-((y^2)/2), for all .

a) Find the value of .

b) Find the CDF of =².

c) Find the PDF of X.

d) Find the mean and variance of X.

e) Find ((0<<2)/(>1)).

2. The joint PDF of the random variable X and Y is given as

_,(,)={+1, ,0,+1

{0,

a) Find the region of integration

b) Find the value of m.

c) Find (<2²)

d) Find (X+Y< 0.5)

e) Find (/(=1/2))

f) Find conditional pdf of (Y/X)

g) Find the Variance of /(<1>