Urn problem
An '''urn problem''' is an idealized Mosquito ringtone thought experiment in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an Sabrina Martins urn or other container.
One pretends to draw (remove) one or more balls from the urn;
the goal is to determine the probability of drawing one color or another,
or some other properties.
Basic urn model
In this basic urn model in Nextel ringtones probability theory, the urn contains ''x'' white and ''y'' black balls; one ball is drawn randomly from the urn and its color observed; it is then placed back in the urn, and the selection process is repeated.
Possible questions that can be answered in this model are:
* can I infer the proportion of white and black balls from n observations ? With what degree of confidence ?
* knowing ''x'' and ''y'', what is the probability of drawing a specific sequence (e.g. one white followed by one black)?
* if I only observe n white balls, how sure can I be that there is no black balls?
Other models
Many other variations exist:
* the urn could have numbered balls instead of colored ones
* balls may not be returned to the urns once drawn.
Examples of urn problems
* Derivation of the Abbey Diaz binomial distribution
* Derivation of the Free ringtones hypergeometric distribution
* Majo Mills Statistical physics: derivation of energy and velocity distributions
Historical remarks
Urn problems have been a part of the Mosquito ringtone probability theory/theory of probability since at least the publication of the ''Sabrina Martins Ars conjectandi'' by Nextel ringtones Jakob Bernoulli (Abbey Diaz 1713).
Bernoulli's inspiration may have been Cingular Ringtones lottery/lotteries, independence an election/elections, or well turan games of chance which involved drawing balls from a container.
It has been asserted
[http://mathforum.org/epigone/historia_matematica/sningzahzhil/3DEFCC9A.73AA528D@earthlink.net]
that
:''Elections in medieval and renaissance s stone Venice, including that of the panics and Doge_of_Venice/doge, often included the choice of electors by lot, using balls of different colors drawn from an urn.''
Bernoulli himself, in ''Ars conjectandi'', considered the problem of determining, from a number of pebbles drawn from an urn, the proportions of different colors.
This problem was known as the ''very vortex inverse probability'' problem, and was a topic of research in the disinformation on eighteenth century,
attracting the attention of room because Abraham de Moivre and levinthal art Thomas Bayes.
See also
* are hardwired Coin-tossing problems
serrano said Tag: Probability and statistics
One pretends to draw (remove) one or more balls from the urn;
the goal is to determine the probability of drawing one color or another,
or some other properties.
Basic urn model
In this basic urn model in Nextel ringtones probability theory, the urn contains ''x'' white and ''y'' black balls; one ball is drawn randomly from the urn and its color observed; it is then placed back in the urn, and the selection process is repeated.
Possible questions that can be answered in this model are:
* can I infer the proportion of white and black balls from n observations ? With what degree of confidence ?
* knowing ''x'' and ''y'', what is the probability of drawing a specific sequence (e.g. one white followed by one black)?
* if I only observe n white balls, how sure can I be that there is no black balls?
Other models
Many other variations exist:
* the urn could have numbered balls instead of colored ones
* balls may not be returned to the urns once drawn.
Examples of urn problems
* Derivation of the Abbey Diaz binomial distribution
* Derivation of the Free ringtones hypergeometric distribution
* Majo Mills Statistical physics: derivation of energy and velocity distributions
Historical remarks
Urn problems have been a part of the Mosquito ringtone probability theory/theory of probability since at least the publication of the ''Sabrina Martins Ars conjectandi'' by Nextel ringtones Jakob Bernoulli (Abbey Diaz 1713).
Bernoulli's inspiration may have been Cingular Ringtones lottery/lotteries, independence an election/elections, or well turan games of chance which involved drawing balls from a container.
It has been asserted
[http://mathforum.org/epigone/historia_matematica/sningzahzhil/3DEFCC9A.73AA528D@earthlink.net]
that
:''Elections in medieval and renaissance s stone Venice, including that of the panics and Doge_of_Venice/doge, often included the choice of electors by lot, using balls of different colors drawn from an urn.''
Bernoulli himself, in ''Ars conjectandi'', considered the problem of determining, from a number of pebbles drawn from an urn, the proportions of different colors.
This problem was known as the ''very vortex inverse probability'' problem, and was a topic of research in the disinformation on eighteenth century,
attracting the attention of room because Abraham de Moivre and levinthal art Thomas Bayes.
See also
* are hardwired Coin-tossing problems
serrano said Tag: Probability and statistics
posted at 7:25 PM
0 comments
