This is markov chains

3) Consider a Markov chain with two stepss = [0,1]. And a transition matrix T = W/ - NI- WIN NI Determine the stationary distribution(s) of this chain. [6 Marks] 4) Consider the probability distribution below, -x0-10-Bx f(x,a,B) = ( ra ; x > 0,a > 0,B> 0 10, elsewhere i. Verify that f(x,a,B) is a complete probability distribution [2 Marks] ii. Find the mean of x [2 Marks] iii. Find the variance of x [2 Marks] 5) Consider a four state Markov chain which has the transition matrix 0 1 - 0 2 a. T = 0010 100 0 0 0 10 b. Show that all states have period 3 [6 Marks] 7