A club models the next period's choices between Activities A and B using \(M=\begin{pmatrix}0.7&0.2\

Question

A club models the next period's choices between Activities A and B using $M=\begin{pmatrix}0.7&0.2\ 0.3&0.8\end{pmatrix}$. Columns represent the current activity (A, then B); rows represent the next activity (A, then B). For example, 0.7 is the proportion of current A members predicted to choose A next period. Each member chooses exactly one activity, and the model assumes no members join or leave. The current numbers are $v=\begin{pmatrix}120\ 90\end{pmatrix}$. Calculate $Mv$.[2] Interpret the result.[2]

Accepted Answer

(a) $\begin{pmatrix}102\ 108\end{pmatrix}$ (b) Predicted next-period choices: A, 102 members; B, 108 members.

Interpreting a one-step redistribution

Interpreting a one-step redistribution

Solution:

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