A Markov chain X₁, X₁, X₂ ... on the states 0, 1, 2 has thetransition probability matrix1 20.2 0.7P 10.2 0.2 0.62 0.6 0.1 0.3and initial distribution Po = P(X₁ = 0) = 0.2, P₁ =P(Xo = 1) = 0.3, and P2 = P(Xo = 2) = 0.5.(1) Compute the two-step transition matrix;(2) What is P(X3 = 1|X₁ = 0)?(3) What is P(X3 = 0, X5 = 2|X₂ = 1)?(4) What is P(Xo = 2, X₂ = 0, X3 = 1)?00 0.1

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Answered: (1) Compute the two-step transition…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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(1) Compute the two-step transition matrix; (2) What is P(X3 = 1|X₁ = 0)? (3) What is P(X3 = 0, X5 = 2|X₂ = 1)? (4) What is P(Xo = 2, X₂ = 0, X3 = 1)?