Linked Questions

3
votes
2answers
5k views

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. ...
3
votes
1answer
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 ...
1
vote
4answers
115 views

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 ...
3
votes
1answer
489 views

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 ...
4
votes
2answers
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 ...
1
vote
4answers
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 ...
4
votes
1answer
134 views

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 ...
0
votes
2answers
295 views

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 ...
2
votes
1answer
89 views

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 ...
1
vote
0answers
352 views

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 ...
3
votes
1answer
113 views

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 $X$ ...
0
votes
1answer
143 views

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 ...
1
vote
0answers
176 views

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 ...
3
votes
2answers
46 views

A question on fundamentals of Probability and Random Variables

Suppose you own 6 shirts. Starting April 1st, you pick a shirt uniformly at random to wear each day. The choice of shirt is independent of one another. Assume that a shirt worn on a given day is ...
0
votes
3answers
59 views

Expected number of lessons to collect the required cards. [closed]

Gottfried has been collecting cards in a competition to win 10 free stats lessons. Each lesson you attend, you get a letter card (S, T or A). To win you need to spell the word (STATS). There is 1000 S,...

15 30 50 per page