Stochastic processes problem.

(3) (a) Prove the following: (b) (i) A stochastic process X = {Xn, Fn, n = 0, 1,2 ...} is a submartin- gale if and only if -X is a supermartingale. It is a martingale if and only if it is both a sub- and supermartingale. (ii) Suppose (Xn) is a submartingale relative to the filtration (Fn). Then for each m