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)).

Only Typing answer

Not a picture