Consider repeated rolling of a fair die, and assume that the different rolls are independent. For i = 1,2,3, 4, 5, denote by N, the minimum number of additional rolls needed for another distinct face (one of the remaining 6-i faces) to show up, after i distinct faces have shown up. Denote by N the minimum number of rolls needed for each of the six faces of the die to show up at least once. (a) Derive the pmf of Nj. Which common distribution is this (specify the name and the value(s) of the parameter(s))? (b) Write N as a suitable function of the N,'s and, based on this representation, determine EN and VN. Hint: In this exercise, you do not have to derive expectations and variances of common distributions-it suffices to look them up.

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