Let {Wt : t > 0} be a Brownian motion, and let { Ft : t 2 0}, be a filtration for this Brownian motion. Show that: (a) Xt = W2 - t is a martingale. (b) St = exp (oWt + (a - ,)t ) is a martingale for a = 0, a submartingale for a > 0 and a supermartingale for a