Examples of Urn Problems
- binomial distribution: the distribution of the number of successful draws (trials), i.e. extraction of white balls, given n draws with replacement in an urn with black and white balls.
- beta-binomial distribution: as above, except that every time a ball is observed, an additional ball of the same color is added to the urn. Hence, the number of total marbles in the urn grows. See Pólya urn model.
- multinomial distribution: the urn contains balls in more than two colors.
- hypergeometric distribution: the balls are not returned to the urn once extracted. Hence, the number of total marbles in the urn decreases. This is referred to as "drawing without replacement", by opposition to "drawing with replacement".
- multivariate hypergeometric distribution: as above, but with balls of more than two colors.
- geometric distribution: number of draws before the first successful (correctly colored) draw.
- negative binomial distribution: number of draws before a certain number of failures (incorrectly colored draws) occurs.
- Statistical physics: derivation of energy and velocity distributions
- The Ellsberg paradox
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