# Markov Chain: Drawing the State Diagram of the Chain

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A particle moves on the states 1, 2, 3, and 4 according to a time-homogeneous Markov chain {Xn ; n ≥ 0 }

with initial distribution p(0) = ( .2, .8, 0, 0 ) and transition matrix : p = [■(.6&.4&0&0@.6&0&.4&0@0&.6&0&.4@0&0&.6&.4)]

a) Draw the state diagram of the chain. Include the transition probabilities in your diagram. (+4)

b) Give P( X1 = 1| X0 = 2) . (+1)

c) Give P( X4 = 2 | X3 = 1) . (+2)

d) Give P( X5 = 4 | X0 = 1, X1 = 2, X2 = 3, X3 = 4, X4 = 3 ) . (+3)

e) Find the unconditional "path" probability P( X0 = 1, X1 = 1, X2 = 2, X3 = 3 ) . (+5)

f) Find p_11^((2)) = P( X2 = 1| X0 = 1) . (+5)

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#### Solution Summary

This solution shows how to draw the Markov chain for the given problem.

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