Determine whether the following processes are Martingales. (W(t) is a

Brownian motion)

(a) X(t) = e

R t

0

cos(u)dW(u)? 1

2

R t

0 (1?sin

2 (u))du

(b) Y (t) = sin(t 2 W(t))

(c) Z(t) = W 5 (t) ? (10W 3 (t) + 15tW(t))t