Dick and Jane have agreed to meet for lunch between noon (0:00 p.m.) and 1:00 p.m. Denote Jane's arrival time by X, Dick's by Y, and suppose X and Y are independent with probability density functions
fX(x)=3x2 for 0<=x<=1, 0 otherwise.
fY(y)=2y for 0<=y<=1, 0 otherwise.
Find the probability that Jane arrives before Dick. That is, find P ( X < Y ).