Problem 1 (Ehrenfest's Diffusion Model). Let N be a container separated into the left ar he right parts by a barrier in the middle. The container is filled with K particles in tota At each time n = 1,2, · . ·, we randomly pick one particle among the K particles and pla t into the other part of the container. Let {Xn}nɛN be the stochastic process where X he number of particles in the left part of the container at time n. The state space of ti process is therefore X = {0,1, ·. . , K}. %3D i) Explain why {X„}n€N is a Markov process.

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