You want to complete a set of 100 baseball cards. Cards are sold in packs of ten.

You want to complete a set of 100 baseball cards. Cards are sold in packs of

ten. Assume that each individual card in the pack has a uniformly random chance of being

any element in the full set of 100 baseball cards. (In particular, there is a chance of getting

identical cards in the same pack.) How many packs of cards should you buy in order to get

a complete set of cards? That is, what is the expected number of cards you should buy in

order to get a complete set of cards (rounded up to a multiple of ten)? (Hint: First, just

forget about the packs of cards, and just think about buying one card at a time. Let N be

the number of cards you need to buy in order to get a full set of cards, so that N is a random

variable. More generally, for any 1 ≤ i ≤ 100, let Ni be the number of cards you need to

buy such that you have exactly i distinct cards in your collection (and before buying the last

card, you only had i − 1 distinct cards in your collection). Note that N1 = 1. Define N0 = 0.

Then N = N100 = ????100 (Ni − Ni−1). You are required to compute EN. You should be able i=1

to compute E[Ni − Ni−1]. This is the expected number of additional cards you need to buy after having already collected i − 1 distinct cards, in order to see your ith new card.)