Question

The joint probability density function of X and Y is given by

f(x,y)={e^-(x+y)   for X>0, y>0      and    0   elsewhere

A. Find the marginal density of X

B. Find the marginal density of Y

C. Find the Conditional density of X given Y

D. Are random variables X and Y independent? State the reason of your answer.

E. Find P(X<.5, y<.5)

F. Find P(X=.5, y<.5)