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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5. Explain what is meant by BLUE estimates and the Gauss-Markov theorem. Mathematics relevant proofs will be rewarded. [:
A Markov chain has two states. • If the chain is in state 1 on a given observation, then it is three times as likely to be in state 1 as to be in state 2 on the next observation. If the chain is in state 2 on a given observation, then it is twice as likely to be in state 1 as to be in state 2 on the next observation. Which of the following represents the correct transition matrix for this Markov chain? О [3/4 2/3 1/4 1/3 O [2/3 1/3 3/4 1/4) о [3/4 2/3 1/3] None of the others are correct 3/4 O [1/4 1/3 2/3. O [3/4 1/4] 1/3 2/3.
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.
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?