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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Suppose that in a survey of five-year-olds, 45% liked the letter A, 54% liked the letter B, and 50% liked the letter of C. 29% liked A and B, 28% liked A and C, 29% liked B and C, and 15% liked all of them. What percentage liked A and B but not the letter C?
Ethan has a bag that contains strawberry chews, apple chews, and lime chews. He performs an experiment. Ethan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Ethan performs the experiment 47 times. The results are shown below: A strawberry chew was selected 36 times. A apple chew was selected 9 times. A lime chew was selected 2 times. If the experiment is repeated 600 more times, about how many times would you expect Ethan to remove a lime chew from the bag? Round your answer to the nearest whole number.
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?
One package contains 5 blue, 4 red and 3 green marbles. We pay $ 14 to draw two marbles at random and without replacement. If we get two blue marbles a prize of $ 20 is won, with two red marbles a prize of $ 30 is won, with two green marbles a prize of $ 30 is won, with two green marbles a prize of $ 50 is won and with any other result they lose the $ 14 they paid to play. Find the expected value of the win in this game. Write your answer in dollars and cents without the $ sign Example: -5.06
A building contractor has a chance to buy an odd lot of 1,000 used bricks at an auction. She is interested in determining the proportion of bricks in the lot that are cracked and therefore unusable for her current project, but she does not have enough time to inspect all 1,000 bricks. Instead, she checks 150 bricks to determine which ones are cracked. What is the population of interest? all building contractors all 1,000 bricks in the lot the rest of the 850 bricks the 150 bricks selected for inspection the rest of the 700 bricks What group constitutes the sample? the 150 bricks selected for inspection all building contractors the rest of the 700 bricks all 1,000 bricks in the lot the rest of the 850 brickS Submit Answer
You are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, three $10-dollar bills, and two $20 dollar bills, and you draw out one bill at a time at random until you have at least $20. If you keep track of each bill as you draw it out of the wallet, how many different ways are there for you to get at least $20?
I need help on both questions. Thank you in advance!
Choosing four people at random from the US population and none of them having diabetes, if 8.3% of the population has diabetes?
You are trying frantically to get dressed, and you need to reach into your sock drawer to get two matching socks in the dark. Your sock drawer contains 20 socks, consisting of 10 matched pairs. All of them are only black or white, and they are loose, disorganized randomly, and not bound together. This means you have 10 black and 10 white socks in your disorganized drawer. This makes 10 total matching pairs of 5 pairs of white and 5 pairs of black. 1. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!) 2. Explain dependent and independent trials
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.

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