A fair die is tossed until all the numbers have been seen at least once. Let...

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A fair die is tossed until all the numbers have been seen at least once. Let N be the number of tosses this requires. Find E(N). [Hint: Let N; be the number of tosses until i different numbers have been seen, i = 1,..., 6. Note that N₁ = 1 and N = No. Find a relationship between E(Ni+1) and E(N;) by conditioning on the outcome of the (N;+1)st toss. Alternatively, consider the joint distribution of N2 - N₁, N3 - N2, ..., N6 - N5.] A fair die is tossed until all the numbers have been seen at least once. Let N be the number of tosses this requires. Find E(N). [Hint: Let N; be the number of tosses until i different numbers have been seen, i = 1,..., 6. Note that N₁ = 1 and N = No. Find a relationship between E(Ni+1) and E(N;) by conditioning on the outcome of the (N;+1)st toss. Alternatively, consider the joint distribution of N2 - N₁, N3 - N2, ..., N6 - N5.]

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