In the basic PĆ³lya urn model, the urn contains x white and y black balls; one ball is drawn randomly from the urn and its color observed.

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Match this urn problem to a distribution

An urn initially contains r red balls and b black balls. A holding area outside the urn initially contain no balls. Balls are randomly chosen from the urn and: the chosen ball and the balls in the ...
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A variation of Polya's urn

Polya's urn model is as follows: you have $a\in \mathbb{Z}_{>0}$ red balls and $b\in \mathbb{Z}_{>0}$ blue balls in a urn. Suppose you pick a red ball. Then you put back $c\in ...
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Multicolored Polya Eggenberger Urn distributions

From an urn containing 1 ball each of $n$ different colours, a ball is drawn, its colour noted and then it is returned to the urn along with $k$ balls of the same colour. what is the limit of the ...
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Number of draws to see every object at least once

I woke up this morning with the following question on my mind: What is (the distribution of) the number of draws you need to sample (with replacement) from an urn with $n$ distinct objects until you ...
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Equilibrium distributions for a finite urn scheme

Given an urn with $n$ (fixed) balls that can be red or black, and given two parameters $0 < p, \, q < 1$, keep doing the following: Flip a $p$-coin. If heads come up, remove a black ball or ...