A stochastic matrix is called doubly stochastic if its columns sum to 1.(a) Let X0, X1,... be a Markov chain on S = {1, ..., 4} with doubly stochastic transition matrix and initialdistribution that is uniform on {1, ..., k}. It has the following transition matrix:1Show that the distribution of X1 is pi = (1)/(4), for all i ∈{1, 2, 3, 4}.(b) Prove that for all doubly stochastic matrices with initial uniform distributions the distribution ofXn = (1)/(k), where k is equal the number of states for a

SOLVED:Determine whether the stochastic matrix P is regular. Then find the steady state matrix X of the Markov chain with matrix of transition probabilities P. P=[ 0.5 0.1 0.5 0.9]

Stochastic Model / Process: Definition and Examples