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…

Answered: C1. A collector wants to collect…

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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Similar questions

Suppose there are 14 people from which you can choose a President, Vice President, and a Treasurer. How many possibilities are there?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 15 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 11 spots labeled $1, 10 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?
event. The first card is a club and the second is a spade.
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You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. ***The image is the example*** Questions: Prove that for all positive integers n ≥ 3, if there are n cards in the deck, you score exactly 1 point with probability 12 and exactly 2 points with probability 13.
15) Use the situation below to answer the question that follows. Team Jet has 7 members who won a school competition. Of these 7, 4 members are randomly picked to receive prizes for winning. The 1st member selected wins a $50 gift card; the 2nd person selected wins a $25 gift card; the 3rd person selected wins a $10 gift card; the 4th person selected wins a $5 gift card. The names of Team Jet's members are represented by the first letter of their first names, as displayed in the following table: Name Frank Gina Harriet Inez Jakob Keven Liu Letter F G H I J K L In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) FGHIJKL Let Lui win the 1st prize, so select L. 2) 3) 4)

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