Each Day, Quintana Watches Exactly One Movie $$\left( \begin{array} { c c c } .2 & .27 & .53 \\.18 & .33 & .59 \\.22 & .1 & .67\end{array} \right)$$

Each day, Quintana watches exactly one movie. She only watches action movies (genre 1), comedies (genre 2), and dramas (genre 3). Let Xᵢ, i=1,… be a sequence of random variables with Xᵢ=n if Quintana watches a movie of genre n on day i. Suppose that {Xᵢ} is a Markov process with probability transition matrix $$\left( \begin{array} { c c c } .2 & .27 & .53 \\.18 & .33 & .59 \\.22 & .1 & .67\end{array} \right)$$ Find the long run proportion of days she watches each genre.

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