Urn Problem - Examples of Urn Problems

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:

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “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)

    “She has problems with separation; he has trouble with unity—problems that make themselves felt in our relationships with our children just as they do in our relations with each other. She pulls for connection; he pushes for separateness. She tends to feel shut out; he tends to feel overwhelmed and intruded upon. It’s one of the reasons why she turns so eagerly to children—especially when they’re very young.”
    —Lillian Breslow Rubin (20th century)