Transition matrix

3. A Markov chain X0, X1, X21," has transition matrix 0123 0 1 0 0 0 1 0.1 0.2 0.5 0.2 2 0.1 0.2 0.6 0.1 3 0.2 0.2 0.3 0.3 p: Conditioned on X0 = 2, calculate the probability that the process never visits state 1. The bivariate distribution of X and Y is described below: X Y 1 2 1 0.22 0.43 2 0.1 0.25 A. Find the marginal probability distribution of X. 1: 32 2: 68 B. Find the marginal probability distribution of Y. 1: 65 2: 35 C. Compute the mean and variance of X. Mean = (1*.32)+(2*.68) Variance = 1.279 C. Compute the mean and variance of Y. Mean = .65+2*.35 Variance =Problem 2: A Markov chain has transition matrix P: [0.2 0.6 0.2 P = 0.1 0.8 0.1 0.1 0.6 0.3 The states of the Markov Chains are {1, 2,3}. For example, the probability that the Markov Chain will be in state 3 after one time step, given that it is in state 1 now, is P(X, = 3 Xo = 1) = 0.2. The initial distribution is a = (0.2,0.3, 0.5). Do all matrix multiplications by hand and find the following: 1. P(X7 = 3 X6 = 2) 2. P(Xg = 2 X1 = 2, Xs = 1, X, =3) 3. P(Xo = 3 X1 = 1) 4. E(X2)