C1. A collector wants to collect football stickers to fill an album.There are n unique stickers to collect. Each time the collector buys asticker, it is one of the n stickers chosen independently uniformly atrandom. Unfortunately, it is likely the collector will end up having"swaps", where he has received the same sticker more than once,so he will likely need to buy more than n stickers in total to fill hisalbum. But how many?(a) Suppose the collector has already got j unique stickers(and some number of swaps), for j = 0, 1, 2, . . .‚ n – 1. Let X,be the the number of extra stickers he buys until getting a newunique sticker. Explain why X, is geometrically distributed, andstate the parameter p = p; of the geometric distribution.(b) Hence, show that the expected number of stickers thecollector must buy to fill his album isnnk=1k(c) The World Cup 2020 sticker album required n = 670 uniquestickers to complete it, and stickers cost 18p each. Using theexpression from (b), calculate the expected amount of moneyneeded to fill the album. You should do this calculation in Rand include the command you used in your answer.(d) By approximating the sum in part (b) by an integral, explainwhy the expected number of stickers required is approximatelyn log n, where log denotes the natural logarithm to base e.

A collector wants to feel a football sticker album, and there are unique stickers to collect. Each…

C1. A collector wants to collect football stickers to fill an album. There are n unique stickers to collect. Each time the collector buys a sticker, it is one of the n stickers chosen independently uniformly at random. Unfortunately, it is likely the collector will end up having "swaps", where he has received the same sticker more than once, so he will likely need to buy more than n stickers in total to fill his album. But how many?