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 atrandom. Unfortunately, it is likely the collector will end up having "swaps", where he has received thesame sticker more than once, so he will likely need to buy more than n stickers in total to fill his album.But how many?(a) Suppose the collector has already got j unique stickers (and some number of swaps). Let X, bethe the number of extra stickers he buys until getting a new unique sticker. Explain why X, isgeometrically distributed, and state the parameter p = p; of the geometric distribution.(b) Hence, show that the expected number of stickers the collector must buy to fill his album isnnk=1(c) The Euro 2020 sticker album required n = 678 unique stickers to complete it, and stickers cost15p each. Using the expression from (b), calculate the expected amount of money needed to fill thealbum. You should do this calculation in R and include the command you used in your answer.(d) By approximating the sum in part (b) by an integral, explain why the expected number ofstickers required is approximately n log n, where log denotes the natural logarithm to base e.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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