answer all 3

Consider a simple, symmetric random walk S,, n 2 0: X1, ..., Xn, .. . independent an identically distributed random variables, Xi : NI- NI and Sn = X1+X2+ ... + Xn. Show that: (a) {Sn, n 2 0} is a martingale w.r.t. Fn = o(Xm, 0 0