Please answer all a b

A player whose initial holding is N bets 1 on each game of a series of independent identical parts. He loses his bet whether he loses or he wins but, if he wins, he gets back k times his stake. It is assumed that the player has a probability p of winning each game independently others. We set Mn = Sn - n (kr 1) for n 20, where Sn represents having of the player after n games. (a) Show first that Mn for n 2 0 is a martingale and T = min {n 2 0: Sn = 0} a stopping time with respect to Sn for n 20, then (b) determine E (T) in the case where kp