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.

1. 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