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### What kind of distribution answers this question?

Suppose that I have $N$ distinct objects, each of which have $1/N$ chance of being drawn. What is the expected number of draws, $D$, to draw at least $x$ of each object (with replacement)? For example:...
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 ...
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### Expectation of the time that a person takes to be in every taxi in town [duplicate]

In a town there $n$ taxis. A person takes one of these taxis every day at random and with replacement. On average, how long does it take before he can claim that he has been in every take in the ...
22 views

### The expected number of n types of coupons have appeared at least once? [duplicate]

There are n different types of coupons and each item must contain one coupon. So what is the expected number of items needed to buy for all n types of coupons have appeared at least once?
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### Additional rolls to see all faces of a die [duplicate]

Suppose that a fair die is rolled repeatedly; different rolls are independent. N is the minimum number of rolls till each of the six faces of the die shows up at least once. Suppose that i ...
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### Calculating the number of trials to get all four outcomes [duplicate]

I was posed the following question recently: Suppose a brand of cereal has four different toys included in their cereal boxes, each with an equal probability of being found: On average, how many ...
18 views

### Combinatorics and statistics question regarding drawing every element [duplicate]

Assuming a set of size X, on average how many attempts would it take to randomly draw every element in the set (returning it back after drawing)? I have a hard time formulating a title for this ...
20 views

### Expected number of tries before all elements of sample space have occurred. [duplicate]

We have a bag with 4 balls, one white, one black, one blue and one red. We are drawing balls with replacement. Find the expected value of the number of tries needed to draw all four colours. More ...
16 views

### How many toys do I need to buy to get the whole set? [duplicate]

I'm collecting toys, they come in blind packs and there are 9 of them. Therefore for the first toy I have a 1.0 probability of getting a toy I haven't had before, then a 8/9, then a 7/9 and so on. On ...
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### Sum of geometric distributions [duplicate]

Imagine that I've got a big $N \times N$ boolean matrix (all entries are $0$ or $1$). At the beginning, the matrix is full of zeros. Then, I execute the following algorithm ...
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### Expected value of removing every ball once [duplicate]

I thought of this question and I somehow I can't figure out an answer Let there be a box with $n$ balls (which have numbers from $1$ to $n$ to that you can distinguish them). When we randomly pick a ...
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### 4 Distinct toys in cereal boxes, on average, how many do I need to open to get all the toys? [duplicate]

here's my question: There are 4 distinct toys in cereal boxes, and each type, independent of prior selections, is equally likely to be in a box. On average, how many cereal boxes would you need to ...
35 views

### How many rolls of an n-sided die before all n values are seen? [duplicate]

I'm currently playing a mobile game where one of the main activities is to collect characters from six different classes. You get new characters in the game by opening crystals, which each give you ...