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-3:r-2y
for 0 < x < y
and fX,Y(x,y) = 0 otherwise. Given that X = 1/2, find the conditional probability that Y > 2/3. In other words, find P(Y > 2/3 | X = 1/2).