Question

Problem 7. Let Sn = X1 + ... + Xn, where Xį are independent with EX; = 0 and Var(X;) = 02. By example 5.3, p. 205, S2 – no2 is a martingale. Let Ta = min{n : Snl > a}. (a) Use Theorem 5.10, to show that E[Ta] > . (b) Show that, for simple random walk, o2 = 1, we have equality.

Theorem 5.10:

Please answer both parts

Answer 1