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1. Consider a Markov chain {Xn,n = following one-step transition matrix 0,1, 2, ...} with state space {1,2,3} and the (0.1 0.1 0.8 P = 0.6 0.4 0.3 0.7 Find the following quantities: (a) P(X1 = 3|Xo = 1). (b) E[X1|Xo = 1]. (c) P(X2 = 1|Xo = 2). (d) P(X1 = 1, X, = 2, X3 = 3| Xo = 1). (e) The stationary distribution ™ = (T1, T2, T3) of the Markov chain. (f) E[X2|Xo = 2]. (g) limn- P".

1. Consider a Markov chain {Xn,n = following one-step transition matrix 0,1, 2, ...} with state space {1,2,3} and the (0.1 0.1 0.8 P = 0.6 0.4 0.3 0.7 Find the following quantities: (a) P(X1 = 3|Xo = 1). (b) E[X1|Xo = 1]. (c) P(X2 = 1|Xo = 2). (d) P(X1 = 1, X, = 2, X3 = 3| Xo = 1). (e) The stationary distribution ™ = (T1, T2, T3) of the Markov chain. (f) E[X2|Xo = 2]. (g) limn- P".

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Consider a Markov chain {Xn,n = 0,1,2, ...} with state space {1, 2, 3} and the following one-step transition matrix (0.1 0.1 0.8 P = 0.6 0.4 0.3 0.7 0 Find the following quantities: (a) P(X1 = 3| Xo = 1). (b) E[X1|Xo = 1]. (c) P(X2 = 1|Xo = 2). (d) P(X1 = 1, X2 = 2, X3 = 3| Xo =1). (e) The stationary distribution T = (T1, T2, T3) of the Markov chain. (f) E[X2|Xo = 2]. (g) limn-+ P.
Transcribed Image Text:1. Consider a Markov chain {Xn,n = 0,1,2, ...} with state space {1, 2, 3} and the following one-step transition matrix (0.1 0.1 0.8 P = 0.6 0.4 0.3 0.7 0 Find the following quantities: (a) P(X1 = 3| Xo = 1). (b) E[X1|Xo = 1]. (c) P(X2 = 1|Xo = 2). (d) P(X1 = 1, X2 = 2, X3 = 3| Xo =1). (e) The stationary distribution T = (T1, T2, T3) of the Markov chain. (f) E[X2|Xo = 2]. (g) limn-+ P.
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