Show that any sequence of independent random variables taking values in the countable set S isa Markov chain. Under what condition is this chain homogeneous?

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Answered: Show that any sequence of independent…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Consider a sequece of iid random variables {§n, n= 0, 1, 2,...} with mass probabilities P(§n = 0) = 0.1, P(§n = 1) = 0.5, and P(§n = 2) = 0.4. Define a Markov chain (X₂)n≥o on the state space S = {0, 1, 2} using the rule Xn = |Xn−1 − Én |• Write the transition matrix for this Markov chain: P = =
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Determine the probability transition matrix ∥Pij∥ for the following Markov chains. Pleaseprovide the solutions step by step and provide a short explanation for each step. Let the discrete random variables ξ1, ξ2, . . . be independent and with thecommon probability mass function
A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.
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Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrix
Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun
Alan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row. Define a Markov chain to model the above problem.
1. Prove that Weiner Process is Markovian (Markov Process).
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Suppose the transition matrix for a Markov Chain is T = stable population, i.e. an x0₂ such that Tx = x. ساله داد Find a non-zero

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Show that any sequence of independent random variables taking values in the countable set S' is a Markov chain. Under what condition is this chain homogeneous?