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

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

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

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