Question

Suppose Alice is sitting at a circular table with 4 chairs labeled {1, 2, 3, 4} and sitting initially at a random chair. Every minute she moves to her left or right at random with equal probability. Consider the Markov chain associated to the sequence of her positions X0, X1, . . . .

1. Write the state space, the distribution of X0 and the distribution of X1.

2. Write the transition matrix.

3. Assume she is at chair one at time t = 0. Write an expression (in terms of numbers Pn, do not evaluate) for the probability that she will be at 1 again at t = 4 and at a

different chair at t = 12.

Suppose Alice is sitting at a circular table with 4 chairs labeled 1, 2,3, 4) and sitting initially at a random chair. Every

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Answer #1

1. As there are 4 chairs so 4 positions or 4 states, namely state 1, state 2, state 3, and state 4. Thus a state variable has0.5 Transition matrix From To 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 X1 0.5 0 0.5 0 0 0.5 0 0.5 0.5 0 0.5 0 4 0.5 0 0.5 0 0 0.Assume she is at chair one at time t 0. Write an expression (in terms of numbers Pn, do not evaluate) for the probability tha

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Suppose Alice is sitting at a circular table with 4 chairs labeled {1, 2, 3, 4} and sitting initially at a random chair. Every minute she moves to her left or right at random with equal probability. C...
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