Consider a Markov Chain with three possible states S = {1,2,3}, that has the following transition matrix. [1/2 1/4 1/4] P = |1/3 [1/2 1/2 2/3 (a) Draw the state transition diagram for this chain. (b) P( X5 = 2 | X4, = 1) (c) P(X3 = 2| X2 = 2) (d) If we know P(Xo = 1) = 1/4, find P(Xo = 1,X1 = 2) (e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2,X2 = 3)

Consider a Markov Chain with three possible states S = {1,2,3}, that has the following transition matrix. [1/2 1/4 1/4] P = |1/3 [1/2 1/2 2/3 (a) Draw the state transition diagram for this chain. (b) P( X5 = 2 | X4, = 1) (c) P(X3 = 2| X2 = 2) (d) If we know P(Xo = 1) = 1/4, find P(Xo = 1,X1 = 2) (e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2,X2 = 3)

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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