Consider the Markov chain with transition matrix P=1/23/401/3011/61/40 1. Show that this is irreducible and even regular. 2. The process is started in state 1 ; find the probability that it is in state 3 after two steps. 3. Find the matrix which is the limit of Pn as n. 4. Write a Python function that runs the Markov chain starting from state 1 and show that the vector p(n) indeed tends toward the stationary distribution. To make it concrete run the chain during N=1000 steps and let ni be the number of time it has been in state i for i=1,2,3. Observe that the vector (n1/N,n2/N,n3/N) is indeed very close to the stationary distribution