Gamblers Ruin a man has $2, which he is going to bet $1 at a time until he either loses
Chapter 10, Problem 23(choose chapter or problem)
Gamblers Ruin a man has $2, which he is going to bet $1 at a time until he either loses all his money or he wins $5. Assume he wins with a probability of 0.45 and he loses with a probability of 0.55. (a) Construct the transition matrix for this game. (b) On the average, how many times will the process be in nonabsorbing states? (c) What is the expected length of the game? (d) What is the probability the man loses all his money or wins $5? Hint: The fundamental matrix T of the transition matrix P is T = D 1.584283 1.062332 0.635282 0.285877 1.298406 2.360738 1.411737 0.635282 0.949001 1.725456 2.360738 1.062332 0.52195 0.949001 1.298406 1.584283T
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer