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### Expected number of trials for all possible outcomes to happen

Suppose that in each trial there are exactly $n$ possible outcomes with probabilities $p_1, \dots, p_n$ which sum to $1$. I wonder what's the expected number of trials for all outcomes to happen at ...
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### Expected number of dice throws to fill out a table.

Say I have a table of numbers ${1,2,3,4,5,6}$. Every time I throw a fair die, if the position in the table is unchecked, it becomes checked and if it is already checked it becomes unchecked. For how ...
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### Expected samples to observe all unique observations

Suppose I have a bag with: $6$ red balls $4$ blue balls $1$ black ball If I sample one ball from the bag at a time, with replacement, what is the expected number of samples required before I observe ...
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### What is the expected number of cards I should buy to have all of them? [duplicate]

Background:My little brother collects cards and tries to complete a book of them, In order to depress him a little I'm trying to compute the number of he need to buy in order to collect all of them,...
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### Different ways to calculate the expected value of getting all faces of a 6 sided die atleast once

Problem Statement: You roll a fair six-sided die until all six numbers have been rolled at least once. What is the expected value of that ? Can you write different ways to solve this problem ?
Let T denote the number of times we have to roll a fair dice before each face has appeared at least once and N denote the number of different faces appearing in the first six rolls. Then $E(T|N=3)=?$ ...
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:...