Calculate the transition probabilities, Basic Statistics

Assignment Help:

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?

 


Related Discussions:- Calculate the transition probabilities

STATISTICS, EIGHT definition of statistics and their scholars

EIGHT definition of statistics and their scholars

Kripsy kreme, How did round trip transactions violatet the revenue recognit...

How did round trip transactions violatet the revenue recognition principle?

Esk jewellery, You are working for the management of ESK Jewellery as a mar...

You are working for the management of ESK Jewellery as a marketing consultant. The main business of ESK Jewellery is the retailing of diamond jewellery. They opened their first sho

Central tendency, List down various measures of central tendency and explai...

List down various measures of central tendency and explain the difference between them?

calculate the chi-square statistic, The table below shows a breakdown of w...

The table below shows a breakdown of women between the ages of 20 to 64 who have had a Pap smear--it shows the number in each age group cross tabulated with the time of their last

Explain Book value, Explain Book value The net quantity at which an advant...

Explain Book value The net quantity at which an advantage or asset group appears on the books of account, as distinguished from its marketplace or intrinsic value where book value

Compute the mean absolute deviation and mean square error, Toyota Motors in...

Toyota Motors introduced a hybrid car Hybrid G in the U.S. market in 2006. In the first three years, the sales of Hybrid G were strong due to the buzz surrounding the hybrid car co

Calculate the monopoly profits and probability , Each firm in a competitive...

Each firm in a competitive research industry can undertake one project at a constant cost, f = $960 to try and develop a certain new product. The inverse demand curve for the new

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd