Question

A Markov chain X0,X1,X2,.. with states 1, 2, 3, has the following transition probability matrix P = .4 .2 .4 .6 .3 .1 0 .5 .5 Suppose that the chain starts at either states 2 or 3 with the same probability, in other words,the initial distribution is p0= [0, .5, .5]. Find (i) P(X0= 2) (1 POINT) (ii) P(X1= 2) (2 POINTS) (iii) P(X?= 2) (2 POINTS) (iii) E3T1 (3 POINTS) (Hint: notice that this matrix, in addition to its rows adding up to 1, also satisfies that its columns add up to 1. This should make finding a left eigenvector for the eigenvalue 1, and therefore, finding the stationary distribution, a very simple task. No MATLAB needed!)

          A Markov chain X0,X1,X2,.. with states 1, 2, 3, has the following transition probability matrix
P = .4 .2 .4
.6 .3 .1
0 .5 .5
Suppose that the chain starts at either states 2 or 3 with the same probability, in other words,the initial distribution is p0= [0, .5, .5].
Find (i) P(X0= 2) (1 POINT)
(ii) P(X1= 2) (2 POINTS)
(iii) P(X?= 2) (2 POINTS)
(iii) E3T1 (3 POINTS)
(Hint: notice that this matrix, in addition to its rows adding up to 1, also satisfies that its columns add up to 1. This should make finding a left eigenvector for the eigenvalue 1, and therefore, finding the stationary distribution, a very simple task. No MATLAB needed!)

A Markov chain X0,X1,X2,.. with states 1, 2, 3, has the following transition probability matrix
P = .4 .2 .4
.6 .3 .1
0 .5 .5
Suppose that the chain starts at either states 2 or 3 with the same probability, in other words,the initial distribution is p0= [0, .5, .5].
Find (i) P(X0= 2) (1 POINT)
(ii) P(X1= 2) (2 POINTS)
(iii) P(X?= 2) (2 POINTS)
(iii) E3T1 (3 POINTS)
(Hint: notice that this matrix, in addition to its rows adding up to 1, also satisfies that its columns add up to 1. This should make finding a left eigenvector for the eigenvalue 1, and therefore, finding the stationary distribution, a very simple task. No MATLAB needed!)

Added by Sarah A.

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