Reference no: EM131130972
A man plays independent repetitions of the following game: at each repetition, he throws a dart onto a circular target. Suppose that the distance D between the impact point of the dart and the center of the target has a U[0,30] distribution. If D ≤ 5, the player wins $1; if 5 Xn be the fortune of the player after n repetitions. Then the stochastic process {Xn, n = 0 , 1 , . . . } is a Markov chain.
(a) Find the one-step transition probability matrix of the chain.
Suppose now that the man never stops playing, so that the state space of the Markov chain is the set {0, ± 1 , ± 2 , . . . } Suppose also that the duration T (in seconds) of a repetition of the game has an exponential distribution with
mean 30. Then the stochastic process {N(t),t ≥ 0}, where N(t) denotes the number of repetitions completed in the interval [0, t], is a Poisson process with rate λ = 2 per minute.
(c) Calculate the probability that the player will have completed at least three repetitions in less than two minutes (from the initial time).
(d) Calculate (approximately) the probability P[N(25) ≤ 50].
|
What is theology
: When you hear the word theology, what comes to your mind?- Besides a passing grade, what do you hope to get out of this course over the next eight modules/weeks?
|
|
Failures of a computer system in the interval
: Let N(t) be the number of failures of a computer system in the interval [0,t]. We suppose that {N(t),t ≥ 0} is a Poisson process with rate λ = 1 per week.
|
|
Discuss about the existence or use of free martins
: What does "viviparous" mean? Why is it mentioned so often in the book? What are people's attitudes towards it and why? What are "free martins?" Discuss your opinion about the existence/use of free martins
|
|
How sensitive is OCF to changes in quantity sold
: Consider a three-year project with the following information: initial fixed asset investment = $710,000; straight-line depreciation to zero over the four-year life; zero salvage value; price = $34.75; variable costs = $22.90; fixed costs = $213,500; ..
|
|
Plays independent repetitions of the following game
: A man plays independent repetitions of the following game: at each repetition, he throws a dart onto a circular target. Suppose that the distance D between the impact point of the dart and the center of the target has a U[0,30] distribution. If D ..
|
|
Create your philosophy of an educational statement
: For this assignment, you will create your philosophy of an educational statement as a current or future educational leader by reflecting on the example provided in Educational Leadership Philosophy
|
|
Develop a thesis pertaining to the assigned film text
: Develop three (3) topic sentences that articulate the major ideas that will comprise the body of your essay. Remember that your topic sentences should clearly state the argument or point to be made in the respective paragraphs.
|
|
What effect do you think the inflation adjusted interest
: What effect do you think the inflation-adjusted interest rate has on the cost of an I-bond in comparison with similar bonds with no allowance for inflation?
|
|
Be received during each of two consecutive
: Let N(t) be the number of telephone calls received at an exchange in the interval [0,t]. We suppose that {N(t) t ≥ 0} is a Poisson process with rate λ = 10 per hour.
|