4 . The matrix
�0.52 0.63�
T � � � is a transition matrix for a Markov chain . �0.48 0.37 �
( a ) Find the values of �
1
and �
2
, the eigenvalues of T , where �1 � �2.
�0.09�
Let v
0
� � � . �0.91�
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13
( b ) Find v
13
, the state probability vector after 13 transitions .
( c ) Find v , the steady state probability vector for this Markov chain .
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