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 minute she moves to her left or right at random with equal probability. C...
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 Xo, Xi, Write the state space, the distribution of Xo and the distribution of X. Write the transition matrix. . .. . 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 minute she moves to her left or right at random with equal probability. Consider the Markov chain associated to the sequence of her positions Xo, Xi, Write the state space, the distribution of Xo and the distribution of X. Write the transition matrix. . .. . 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.