Consider a Markov chain in which X, = 0 if it rains on day i, and otherwise, X, = 1. Denote the day-to-day transition probabilities by PAk = Pr(state k on day i | state j on day i - 1), j, k = 0, 1. Suppose that the probability state transition matrix is P = 0.8 0.2 0.4 0.6 Suppose that it rains on Monday, e.g., Xo = 0. Use simulation to find the probability that it rains on Wednesday, e.g., estimate Pr(X2 = 0|X, = 0). [You may have to simulate the process a bunch of times in order to estimate this probability.]
a. 0
b. 0.64
c. 0.72
d. 0.8
e. 1