Problem 3 Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix [1/2 1/4 1/41 P = |1/3 [1/2 1/2 2/3 %3D a. Draw the state transition diagram for this chain. 1 b. If we know P(X1 = 1) = P(X1 = 2) = -, find P(X, = 3, X2 = %3| %3D 4 2, X1 = 1)
Problem 3 Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix [1/2 1/4 1/41 P = |1/3 [1/2 1/2 2/3 %3D a. Draw the state transition diagram for this chain. 1 b. If we know P(X1 = 1) = P(X1 = 2) = -, find P(X, = 3, X2 = %3| %3D 4 2, X1 = 1)
A First Course in Probability (10th Edition)
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INEN435 Stochastic Operations Research
Homework 3
Problem 3
Consider the Markov chain with three states, S={1,2,3}, that has the
following transition matrix
[1/2 1/4 1/41
P = |1/3
1/2 1/2
2/3
0.
a. Draw the state transition diagram for this chain.
b. If we know P(X1 = 1) = P(X1 = 2) = ÷, find P(X1 = 3, X2 =
1.
2, X, = 1)
Problem 4
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