QUESTION 1 Consider a Markov chain with (one-step) transition probability matrix P= How many communicating classes does the Markov chain have? QUESTION 2 Consider a Markov chain with (one-step) transition probability matrix P= " . How many communicating classes does the Markov chain have? QUESTION 3 Consider a Markov chain with (one-step) transition probability matrix P=|9 . What is the period of state 0? (If the state is aperiodic, enter 1.)60. The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 .4 .2 .2 P = .25 .2 .1 If Xo = 1 (a) find the probability that state 3 is entered before state 4; (b) find the mean number of transitions until either state 3 or state 4 is entered.Assume P is the transition probability matrix of a Markov chain with three states A, B and C 2 3 .5 P = 4.6 0 .4 .4 .2 What is the probability of going from state A to B in one step? What is the probability of going from state C to A in exactly two steps? To what matrix will the n-step transition probability matrix converge when n is very large? Your solution should be accurate to two decimal places.1 0 3 8 LetA= 0 3 D 10+10 3 D 1 (a) Find the spectral decomposition of A. (b) Find the spectral decomposition of 3'4 = 2:0 3:11.211"