a male and a female go to a 2-table restaurant on the same day. each day the mal

Question

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:

[0.3 0.7

0.7 0.3]

[0.4 0.6

0.6 0.4]

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

Explanation / Answer

The possible states for the markov chain are: {Both sit together, Male sites at Table 1 and Female at Table 2, Male sits at Table 2 and Female at Table 1}

Because the probability of transition to a state is dependent on only the previous state and not on the entire history of the chain

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