6. The Laplace diffusion model considers two boxes containing N balls each, N 2 2. At the moments n = 1, 2, ... one ball from each box is chosen uniformly at random and placed in the other box. Assume at moment 0 the first box contains / white balls and the second box contains / black balls. Define a Markov chain Xn =(number of black balls inside the first box at the moment n), n = 0, 1, .... (a) Write down the one-step transition probability matrix for {Xn}n=0,1,.... What is the state space for this Markov Chain? (b) Find E(Xn+1|Xn), n=0,1,.... (c) Prove that limn - E(Xn) = N/2