2.2 Let X. X₁.... be a Markov chain with transition matrix 1 2 3 1 0 1/2 1/2) 2 1 0 0 3 1/3 1/3 1/3) and initial distribution a = (1/2.0, 1/2). Find the following: (a) P(X₂ = 1|X₁ = 3) (b) P(X₁ = 3, X₂ = 1) (c) P(X₁ = 3|X₂ = 1) (d) P(Xo = 1|X₁ = 3₁X4 = 1, X = 2)

2.2 Let X. X₁.... be a Markov chain with transition matrix 1 2 3 1 0 1/2 1/2) 2 1 0 0 3 1/3 1/3 1/3) and initial distribution a = (1/2.0, 1/2). Find the following: (a) P(X₂ = 1|X₁ = 3) (b) P(X₁ = 3, X₂ = 1) (c) P(X₁ = 3|X₂ = 1) (d) P(Xo = 1|X₁ = 3₁X4 = 1, X = 2)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

2.2 Let X. X₁.... be a Markov chain with transition matrix
1 2 3
10
1/2 1/2)
2 1
0
0
3 1/3 1/3 1/3)
and initial distribution a = (1/2.0, 1/2). Find the following:
(a) P(X₂ = 1|X₁ = 3)
(b) P(X₁ = 3, X₂ = 1)
-
(c) P(X₁ = 31X₂ = 1)
(d) P(Xo = 1|X₁ = 3.X4 = 1.X₂ = 2)

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