8) a) Suppose {Yn, n 1} is a sequence of iid random variables with distribution...

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8) a) Suppose {Yn, n ≥ 1} is a sequence of iid random variables with distribution P(Yn= k) = ak, Define Xo = 0 and Xn = max{Y₁, Y2, ..., Yn}, n = 1,2,3,... Show that {Xn, n = 1,2,...} is a DTMC and display its transition probability matrix. b) k = 1,2,3..., M M+1 Suppose that the probability distribution for Yn is given by ak = , k = 1,2,..., M. Calculate, the expected time until the process reaches the absorbing state M. 8) a) Suppose {Yn, n ≥ 1} is a sequence of iid random variables with distribution P(Yn= k) = ak, Define Xo = 0 and Xn = max{Y₁, Y2, ..., Yn}, n = 1,2,3,... Show that {Xn, n = 1,2,...} is a DTMC and display its transition probability matrix. b) k = 1,2,3..., M M+1 Suppose that the probability distribution for Yn is given by ak = , k = 1,2,..., M. Calculate, the expected time until the process reaches the absorbing state M.