# Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 02

MATH152 April 2017
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### Question B 02

For each matrix below left, interpret the matrix as a probability transition matrix, and match it to its corresponding equilibrium probability on the right. One mark each. Note that answers in the list (I)-(VII) may be a match more than once or not at all.

(A) ${\displaystyle {\begin{bmatrix}1/3&2/3\\2/3&1/3\end{bmatrix}},}$ (B) ${\displaystyle {\begin{bmatrix}1/2&1/2\\1/2&1/2\end{bmatrix}},}$ (C) ${\displaystyle {\begin{bmatrix}1/2&1/2\\2/3&1/3\end{bmatrix}}}$, (D) ${\displaystyle {\begin{bmatrix}9/10&0\\1/10&1\end{bmatrix}}}$, (E) ${\displaystyle {\begin{bmatrix}1&0\\0&1\end{bmatrix}}}$,

(I) ${\displaystyle {\begin{bmatrix}0\\1\end{bmatrix}}}$, (II) ${\displaystyle {\begin{bmatrix}1\\1\end{bmatrix}}}$, (III) ${\displaystyle {\begin{bmatrix}1/2\\1/2\end{bmatrix}}}$, (IV) ${\displaystyle {\begin{bmatrix}1/3\\2/3\end{bmatrix}}}$, (V) ${\displaystyle {\begin{bmatrix}9/10\\1/10\end{bmatrix}}}$,

(VI) not a probability transition matrix, (VII) equilibrium probability not in the list, (VIII) no equilibrium probability

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