8. Prove that for an irreducible Markov chain with M + 1 states, it is possible to go from one state to another in at most M steps. 9. A virus is found to exist in N different strains and in each generation either stays the same or mutates into another strain with probability p/(N 1). Show that the probability that the strain in the n-th generation is the same as that at time zero is 1+|1|1 1 JUN.\" .N N Ni' [Hint: Model this as a 2-state Markov process with the two states being \"initial strain\" and \"other strain\" ]