Consider a Markov chain {Xn}n≥0 having the following transition diagram:For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}.Find the period of stateFind f33 and f22.Starting at state 3, find the probability that the chain is absorbed into R1.Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R1 or R2. Note: there are missing transition probabilities for this chain, but no impact for your solution. 1251/21/4341/21/47

*Answer: *a Period of any state i is given by, C(i)= gcd{Ri} period of state 3: C(3)= gcd{3,4}=…

Consider a Markov chain {Xn}n≥0 having the following transition diagram: For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}. Find the period of state Find f33 and f22. Starting at state 3,

Consider a Markov chain {Xn}n≥0 having the following transition diagram: For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}. Find the period of state Find f33 and f22. Starting at state 3,

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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Question

Consider a Markov chain {X_n}_n≥₀ having the following transition diagram:

For this chain, there are two recurrent classes R₁ = {6, 7} and R₂ = {1, 2, 5}, and one transient class R₃ = {3, 4}.

Find the period of state
Find f₃₃ and f₂₂.
Starting at state 3, find the probability that the chain is absorbed into R₁.
Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R₁ or R₂.

Note: there are missing transition probabilities for this chain, but no impact for your solution.

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