Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 60
1 . The matrix
�0.05 0.3�
T � � � is a transition matrix for a Markov chain . �0.95 0.7�
( a ) Find the characteristic polynomial of T . [ 2 ]
( b ) Hence , write down the values of �
1
and �
2
, the eigenvalues of T , where �1 � �2. [ 2 ]
( c ) Find v , the steady state probability vector for this Markov chain . [ 2 ]
2 . The matrix
�0.5 0.15�
T � � � is a transition matrix for a Markov chain . �0.5 0.85�
( a ) Find the characteristic polynomial of T . [ 2 ]
( b ) Hence , write down the values of �
1
and �
2
, the eigenvalues of T , where �1 � �2. [ 2 ]
( c ) Find v , the steady state probability vector for this Markov chain . [ 2 ]
3 . The matrix
�0.17 0.9�
T � � � is a transition matrix for a Markov chain . �0.83 0.1�
( a ) Find the values of �
1
and �
2
, the eigenvalues of T , where �1 � �2.
�0.5�
Let v
0
� � � . �0.5�
( b ) Find v
8
, the state probability vector after 8 transitions .
( c ) Find v , the steady state probability vector for this Markov chain .
[ 3 ]
[ 2 ]
[ 2 ]
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