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### How many rolls of a $k$-sided dice should you expect to make before all numbers $1, 2,\dotsc, k$ have been seen at least once? [duplicate]

How many rolls of a $k$-sided dice should you expect to make before all numbers $1, 2,\dotsc, k$ have been seen 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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### Expected number of rolls to roll every number [duplicate]

If I am rolling I die until I roll every number at least once, what is the expected value of times that I will need to roll the die? After a brief computer simulation, I got 15. But why is this the ...
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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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### 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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### 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 ...
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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 ...
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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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### Expected minimum size of multinomial distribution that includes at least one value of each class [duplicate]

Suppose I have a vector and I include a new item on it at every time step. This item has one of $k$ different classes, each class has probability $\frac{1}{k}$ of being selected. Suppose now I stop ...
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### 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 ...
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### 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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### 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 ...
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### A question about Poker (and probability in general)

Okay, so I've been thinking about this question for a long time, and I'm starting to think that there isn't an answer. So please read the question, and if there is an answer, tell how you came to it, ...
In the coupon collector's problem, let $T_n$ denote the time of completion for a collection of $n$ coupons. At time $T_n$, each coupon $k$ has been collected $C_k^{n}\geqslant 1$ times. Consider how ...