Markov chain X(t) ∈ {A, B, C} with transition rates [ . 2 2 ]Q= [ 1 . 3 ] [ 5 0 1 ]a) Fill in the missing numbers in the diagonal (marked as "·")b) What is the expected length of a stay in Atlanta? That is, let T_A(T sub A) denote the length of a stay in Atlanta. Find E(T_A).c) For a trip out of Atlanta (that is, jumps out of Atlanta), what is the probability of itbeing a trip to Chicago? Let P_AC denote that probability.d) Find the stationary distribution (πA,πB,πC).What fraction of the year does the salesman on average spend in Atlanta?e) What is his average number nAC of trips each year from Atlanta to Chicago?