1. Consider the following gambler’s ruin problem. A gambler bets $1 on each play of a game. Each…


1. Consider the following gambler’s downfall height. A gambler bets $1 on each indicate of a recreation. Each date, he has a appearance p of seductive and appearance q _ 1 _ p of losing the dollar bet. He achieve remain to indicate until he goes broke or nets a fortune of T dollars. Let Xn illustrate the number of dollars enriched by the gambler behind the nth indicate of the recreation. Then {Xn} is a Markov tie. The gambler starts delay X0 dollars, where X0 is a positive integer short than T. (a) Construct the (one-step) transition matrix of the Markov tie. (b) Perceive the classes of the Markov tie. (c) Let T _ 3 and p _ 0.3. Using the notation of Sec. 16.7, perceive f10, f1T, f20, f2T. (d) Let T _ 3 and p _ 0.7. Perceive f10, f1T, f20, f2T.