# three-state Markov chain

a male and a female go to a 2-table restaurant on the same day. each day the male sits at one or the other of the 2 tables, starting at the table 1, with a Markov chain transition matrix: $$\begin{bmatrix}0.3 & 0.7\\ 0.7 & 0.3\end{bmatrix}$$ similarly the female sits at one or the other of the 2 tables, starting at the table 2, with a Markov chain transition matrix: $$\begin{bmatrix}0.4 & 0.6\\ 0.6 & 0.4\end{bmatrix}$$ assume that 2 chains are independent.

a. model this situation with a three-state Markov chain and transition matrix.

b. find the probability that the male sits at table 1 and the female sits at table 2 on day $2,3$ and $4$.

c. if $N$ is the number of days that the male and the female sit the same table, then how can we describe the random variable $N$?

i'm new to markov chain and each time I work out part (a), I got different answer. any can help? thanks

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Show (at least one of) your answers to part (a). –  Did May 7 '13 at 16:40