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1.67. Roll a fair die repeatedly and let Y1,Y2, be the resulting numbers. Let Xn={Y1,Y2,,Yn} be the number of values we have seen in the first n rolls for n1 and set X0=0. Xn is a Markov chain. (a) Find its transition probability. (b) Let T=min{n:Xn=6} be the number of trials we need to see all 6 numbers at least once. Find ET..

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1.67. Roll a fair die repeatedly and let Y1,Y2, be the resulting numbers. Let Xn={Y1,Y2,,Yn} be the number of values we have seen in the first n rolls for n1 and set X0=0. Xn is a Markov chain. (a) Find its transition probability. (b) Let T=min{n:Xn=6} be the number of trials we need to see all 6 numbers at least once. Find ET.

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