Let A and B be random variables with the vector (A, B) uniformly distributed on the region R {(a, b) 0 < b < a < 1}.
(a) Find the joint probability density function of (A, B), and find Pr(A+B < 1).
(b) Find the marginal probability density function f(A), and find E(A).
(c) Find the conditional probability density function f(B|A).