Calculate the transition probabilities, Basic Statistics

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

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
Related Questions
Calculate Correlation coefficient for X and Y, Statistics Homework • Variable X x • Variable Y y • Calculate: • z-scores for all values in the variables • correlation coefficien

The screening test for the hep-c virus works by detecting the presence of antibodies to the virus. However, some non-HCV proteins can trigger a false positive, at a probability of

A.Austria invested cash $1,000 and a type writer $2,500

A researcher is interested in the relationship between fathers' performance in high school and their children's social skills.  She obtains the high school transcripts of fathers a

how are financial instruments recognised in financial reports in the past and present?

The waiting time for an incoming call at the front desk of mathematics Department follows an exponential distribution. During business hours, the average of the waiting times is 10

A sample of 40 golfers showed that their average on a particular course was 94 with a standard deviation of 6. a. Find the 95% confidence interval of the mean score for all golf

Problem 1 . Let X 0 ;X 1 ;X 2 . . . be a Markov chain with state space f1; 2g and transition probabilities given as follows: p 11 = 0:3; p 12 = 0:7; p 21 = 0:5; p 22 = 0:5: