Suppose that B(t) is standard Brownian motion. (a) Fix 0 < t < 1. What is the joint density of B(t), B(1) B(t)? (b) What the joint density of B(t), B(1)? (c) What is the conditional density of B(t) given B(1). (d) Give a simple formula for W(t) B(t) E(B(t)|B(1)). (e) For 0 < s < t < 1 compute Cov(W(s), W(t)).