Let X and Y be two random variables whose joint probability

Let X and Y be two random variables whose joint probability density function is given by

f(x,y)=1/2, x>0, y>0, x+y<2. and o elsewhere.

Let U=y-x (note that U could be positive or negative).

a) find the distibution function of U.

b) using the result in (a), or otherwise, find the probability density function of U.

Solution