Every day, a student calls his mother and then (afterwards) calls his girlfriend. Let X be the time (in hours) until he calls his mother, and let Y be the time (in hours) until he calls his girlfriend. Since he always calls his mother first, then X < Y. So let the joint density of the time be
fX,Y(x,y) = 10e-3x-2y
for 0 < x < y,
and fx,y{x,y) = 0 otherwise.
Let Z = |Y - X| be time in between the beginning of the two calls.
a. Find E(Z).
b. Find Var(Z).