Problem 2. Consider the following gamblers ruin problem. A gambler bets $1 on each play of a game. Each time, he has a probability p of winning and probability q=1-p of losing the dollar bet. He will continue to play until he goes broke or nets a fortune of T dollars. Let X denote the number of dollars possessed by the gambler after the n-th play of the game. Then +1 = (X,+1 with probability p X-1 with probability 1-p Xn+1 X for X=0 or X-T = for 0