Please Help! Markov Chain 1. The problem statement, all variables and given/known data Let X0 be a random variable with values in a countable set I. Let Y1, Y2, ... be a sequence of independent random variables, uniformly distributed on [0, 1]. Suppose we are given a function G : I x [0, 1] -> I and define inductively for n >= 0, Xn+1 = G(Xn, Yn+1). Show that (Xn)n>=0 is a Markov chain and express its transition matrix P in terms of G. 2. Relevant equations 3. The attempt at a solution I know that I need to show that Xn+1 depends on Xn by checking the condition in the definition of Markov chain, and then try to find some formula for P(Xn+1 = j | Xn=i) in terms of G. Actually, my background for Markov chain lacks a little, so I have no how I find some formula for P in terms of G.. How do I handle terms of G? Anybody give me some hints or answer?