Let the joint probability density function of random variables X and Y be given by f(x,y) = 2 if 0 <= y <= x <= 1 and 0 otherwise a) calculate the marginal probability density functions. f(x) = 2x f(y) = 2-2y b) find E(X) and E(Y). E(X) = 2/3 E(Y) = 1/3 c) calculate P(X<1/2) , P(X<2Y) and P(X=Y). P(X<1/2) = integral from 0 to 1/2 of 2x dx = 1/4 but as for the other 2 I have no idea on how to do them. do they also involve the marginal distribution functions? Any help as always is greatly appreciated. Thanks.