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
Read more about this topic: Urn Problem
Famous quotes containing the words examples of, examples and/or problems:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)