Suppose that you are told to toss a die until you have observed each of the six faces
Chapter 5, Problem 5.88(choose chapter or problem)
Suppose that you are told to toss a die until you have observed each of the six faces. What is the expected number of tosses required to complete your assignment? [Hint: If Y is the number of trials to complete the assignment, Y = Y1 + Y2 + Y3 + Y4 + Y5 + Y6, where Y1 is the trial on which the first face is tossed, Y1 = 1, Y2 is the number of additional tosses required to get a face different than the first, Y3 is the number of additional tosses required to get a face different than the first two distinct faces, ..., Y6 is the number of additional tosses to get the last remaining face after all other faces have been observed. Notice further that for i = 1, 2,..., 6, Yi has a geometric distribution with success probability (7 i)/6.]
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