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### The coupon collectors problem [closed]

Each box of a certain breakfast cereal contains one of ten different coupons, each with the same probability. We win a prize if we manage to obtain a complete collection of all the different coupons. ...
622 views

### How long does it take to complete a sticker album?

We are collecing stickers in chocolate bars and whenever we open a bar we get a random new sticker. There are many different stickers and we try to collect them all. We open the first bar and get a ...
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### Number of attempts to see all faces $1, 2, 3, …, 6$ when rolling a dice? [closed]

Recently I have been thinking about the following random experiment: we repeatedly roll a dice until we see all the faces $1, 2, 3, 4, 5, 6$ of the dice at least once. Let $X$ = number of attempts ...
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### Expected number of rolls on a die until each face has appeared at least twice

Note: The die is fair, normal 1 - 6 die. So I understand that the expected number of rolls until each face occurs is 14.7 by the following post: Expected time to roll all 1 through 6 on a die but ...
607 views

### What is the probability of rolling $n$ dice until each side appears at least once?

We roll a die until each side appears at least once, then we stop. What is the probability of rolling exactly $n$ dice? I guess the answer is $$6-6\left(\dfrac{5}{6}\right)^n\;,$$ but this may ...
541 views

### Find the expected number of steps needed until every point has been visited at least once.

The complete graph on {1,...,N} is the simple graph with these vertices such that any pair of distinct points is adjacent. Let $X_{n}$ denote the simple random walk on this graph and let T be the ...
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### How many correct answers does it take to fill the Trivial Pursuit receptacle?

My friends and I likes to play Trivial Pursuit without using the board. We play it like this: Throw a die to determine what color you get to answer. Ask a question, if the answer is correct you get ...
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### Expected number of students problem?

Suppose that in a class of 50 students, the instructor calls on students to answer questions, for each question selecting one student at random and without consideration of whom he has called on in ...
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### Let $X$ be the number of times a die must be rolled to get all $6$ possible outcomes. What is the variance of $X$?

Just started a course in probability when I stumbled upon this question. Now, I know that one formula for variance is: $$\text{Var}(X)= E(X^2) - (E(X))^2$$ I understand that, in general, the ...
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### Solution to rarity-generalized coupon-collector's problem? [duplicate]

Possible Duplicate: A Question About Dice I was reading " Expected time to roll all 1 through 6 on a die " and it got me thinking... There are various ways to generalize the coupon-collector's ...
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### Is there a name for this distribution? (generating until all numbers appear)

A computer program generates a number between $1$ and $n$ every second ( there is a $1/n$ probability for each number ). It continues until all $n$ possible numbers were generated. Let $X$ ...
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### Statistics: convergence in probability

Suppose that you are trying to collect a complete set of $n$ baseball cards. Suppose you buy them one at a time and each time you get a randomly chosen card. Let $N_n$ be the number of cards you have ...
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### Coupon collector problem: expected number to roll all $1$ through $n$ on an unfair $n$-sided die

I have a question about the coupon collector problem. What is the expected number to roll all $1$ through $n$ on an unfair $n$-sided die? Alice rolls a $n$-sided dice until it shows all sides ...