The random variables , $1, 2,... are independent and identically distributed with distribution P( = 0) = 1/4 and P(§ = j) = c/j for j = 1,2,3. Let Xo = 0 and Xn = max($₁,..., En) for n = 1, 2,.... (a) What value must c take? (b) Explain why {Xn, n = 0, 1, 2,...} is a Markov chain. (c) Write down the transition matrix.

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