An exponential distribution with mean equal

Assignment Help Basic Statistics
Reference no: EM131131049

We consider the particular case of the gambler's ruin problem for which fc = 4 and p = 1/2. Suppose that the length (in minutes) of a play (the outcome of which is the player's winning or losing $1) has an exponential distribution with mean equal to 1/2. Moreover, when the player's fortune reaches $0 or $4, he waits for an exponential time (in hours) with mean equal to 2 before starting to play again, and this time is independent of what happened before. Finally, suppose that the player has $1 when he starts to play again if he was ruined on the last play of the preceding game and that he has $3 if his fortune reached $4 on this last play.

Let X{t), for t ≥ 0, be the player's fortune at time t. The stochastic process {X(t),t ≥ 0} is a continuous-time Markov chain.

(a) (i) Is the process {X(t),t ≥ 0} a birth and death process? If it is, give its birth and death rates. If it's not, justify.

(ii) Answer the same question if the player always starts to play again with $1, whether his fortune reached $0 or $4 on the last play of the previous game

(b) (i) Write, for each state j , the Kolmogorov backward equation satisfied by the function Po,j(t).

Reference no: EM131131049

Questions Cloud

Calculate the average time that the process spends : We consider a system composed of three components placed in parallel and operating independently. The lifetime Xi(in months) of component I has an exponential distribution with parameter A, for i = 1,2,3.
The following probability density function : Let {N(t),t > 0} be a counting process such that N(0) = 0. When the process is in state J, the next state visited will be j + 1, for all j ≥ 0. Moreover, the time τj that the process spends in state j has the following probability density function
Expain the relevant costs for the expansion decision : From the scenario for Katrina's Candies, determine the relevant costs for the expansion decision, and distinguish between the short run and the long run costs.
Write an essay on relationships and teen pregnancy issues : Write an essay of 6 pages on the following topic:- Relationships and Teen Pregnancy Issues
An exponential distribution with mean equal : We consider the particular case of the gambler's ruin problem for which fc = 4 and p = 1/2. Suppose that the length T (in minutes) of a play (the outcome of which is the player's winning or losing $1) has an exponential distribution with me..
Discuss whether or not qualitative research methodology : Discuss the potential advantages and disadvantages of qualitative research methodology for your dissertation topic or topic area. (Research is not required to support your conclusions.)
Representation of male and female characters : A comparison of the representation of male and female characters in a specific movie genre - Two protagonists from two of your favorite books or novels
Give examples of required rates of return that would make : Assume a 5-year Treasury bond has a coupon rate of 4.5%.a. Give examples of required rates of return that would make the bond sell at a discount, at a premium, and at par.
Protagonists from two of your favorite books or novels : Comparison and contrast essay on your selected topic that incorporates at least two peer-reviewed academic sources. The rough draft should contain no more than 1,100 words, not counting the title and references pages.

Reviews

Write a Review

Basic Statistics Questions & Answers

  Statistics-probability assignment

MATH1550H: Assignment:  Question:  A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..

  What is the least number

MATH1550H: Assignment:  Question:     what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?

  Determine the value of k

MATH1550H: Assignment:  Question:     Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form

  What is the probability

MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?

  Binomial distributions

MATH1550H: Assignment:  Questions:  Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.

  Caselet on mcdonald’s vs. burger king - waiting time

Caselet on McDonald’s vs. Burger King - Waiting time

  Generate descriptive statistics

Generate descriptive statistics. Create a stem-and-leaf plot of the data and box plot of the data.

  Sampling variability and standard error

Problems on Sampling Variability and Standard Error and Confidence Intervals

  Estimate the population mean

Estimate the population mean

  Conduct a marketing experiment

Conduct a marketing experiment in which students are to taste one of two different brands of soft drink

  Find out the probability

Find out the probability

  Linear programming models

LINEAR PROGRAMMING MODELS

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