Consider a person who repeatedly plays a game of chance (gambling)with two results possible (win or lose) with a probability p = 0, 3 to win. If the person has bet x amount and if he wins, he take back his x dollars and he receives another x dollars. Otherwise, heloses his bet. Suppose that each game, the person chooses to bet the amount as follows: if he has less than $ 3 in hand, he put all his money. Otherwise, since his goal is to have $ 5, he put the difference between $ 5 and what it was in his pocket. The continues to play until he found with 0 or $ 5 in his pocket, then stop playing. Let Xnbe the pocket amount (in whole dollars) only after the game, and assume that X0 the initial money of the player, is an integer uniformly distributed between 1 and 4.

(A) Construct the matrix of transition probabilities of the Markov chain {Xn, n = 0, 1, 2,. . .}.

(B) What is the probability that the game ends on the first try?

(C) If the game ends in the first test, what is the probability that the player is ruined?

(D) If the game continues after the first test, then what is the expected wealth of the player?

(E) What is the probability that the player has $ 3 or more after playing twice?

 

Posted Date: 3/26/2013 7:59:08 AM | Location : United States

Ask an Expert

Related Discussions:- Calculate the transition probabilities, Assignment Help, Ask Question on Calculate the transition probabilities, Get Answer, Expert's Help, Calculate the transition probabilities Discussions

Write discussion on Calculate the transition probabilities
Your posts are moderated

Write your message here..

Related Questions

Definition of mode, what is definition of Mode? what is definition of Mode?

Explanation of the statistical analyses, Introduction Background inform... Introduction Background information so the reader can better grasp the analyses you are going to present. This can include anything that puts the analyses into perspective for

Cost accounting test, i need someon to help me do my cost accounting test i need someon to help me do my cost accounting test

What is owner’s equity, What is owner’s equity? Owner’s value is on... What is owner’s equity? Owner’s value is one of the three primary elements of a single proprietorship’s stability piece and bookkeeping situation. Owner’s value symbolizes

Cost of accounting, what are different method of classifying overhead? indi... what are different method of classifying overhead? indicate the advantag

Time series, method of measuring trend method of measuring trend

#mean, Uses of mean Uses of mean

Limitation of the accounting, Limitation of the Accounting. It informati... Limitation of the Accounting. It information only accounting purchase, it is restricted to the accounting purchase only, and for example other elements which are not having any

Derive the pure strategy nash equilibrium, There are two firms competing in... There are two firms competing in quantity. Firm 1 and 2 set their quantities supplied, q1 and q2, respectively. The production costs are zero. The market price is given by

Payroll, is about deductions is about deductions