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 X_{n+1}=\left\{\begin{array}{l} X_{n}+1 \text { with probability } p \\ X_{n}-1 \text { with pro ability } 1-p \end{array} \quad \text { for } 0