“hypergeometric distribution”的概念、定义、翻译、参考文献-科学参考

hypergeometric distribution

Mathematics

Suppose that, in a set of N items, M items have a certain property and the remainder do not. A sample of n items is taken from the set. The discrete probability distribution for the number r of items in the sample having the property has probability mass function given by $Pr (X = r) = \frac{^{M} C_{r}^{N - M} C_{n - r}}{^{N} C_{n}}$ where r runs from 0 up to the smaller of M and n. This is called a hypergeometric distribution. The mean is $\frac{n M}{N}$ , and the variance is

$\frac{n M (N - M) (N - n)}{N^{2} (N - 1)} .$

Statistics

The distribution of the number of ‘successes’ when sampling without replacement from a finite population each of whose members is classified as either a ‘success’ or a ‘failure’. As an example, suppose that an urn contains N balls of which w are white. Suppose n balls are taken from the urn at random and without replacement, and let the random variable X be the number of white balls obtained. Then X has the hypergeometric distribution given by $hypergeometric distribution$ The initial derivation of the distribution was published by de Moivre in 1711. The mean of the distribution is nw/N and the variance is $hypergeometric distribution$ For large values of N the hypergeometric distribution may be approximated by the binomial distribution B(n, p), where p = w/N, since in this case sampling without replacement is approximately equivalent to sampling with replacement.

单词	hypergeometric distribution
释义	hypergeometric distribution Mathematics Suppose that, in a set of N items, M items have a certain property and the remainder do not. A sample of n items is taken from the set. The discrete probability distribution for the number r of items in the sample having the property has probability mass function given by $Pr (X = r) = \frac{^{M} C_{r}^{N - M} C_{n - r}}{^{N} C_{n}}$ where r runs from 0 up to the smaller of M and n. This is called a hypergeometric distribution. The mean is $\frac{n M}{N}$ , and the variance is $\frac{n M (N - M) (N - n)}{N^{2} (N - 1)} .$ Statistics The distribution of the number of ‘successes’ when sampling without replacement from a finite population each of whose members is classified as either a ‘success’ or a ‘failure’. As an example, suppose that an urn contains N balls of which w are white. Suppose n balls are taken from the urn at random and without replacement, and let the random variable X be the number of white balls obtained. Then X has the hypergeometric distribution given by $hypergeometric distribution$ The initial derivation of the distribution was published by de Moivre in 1711. The mean of the distribution is nw/N and the variance is $hypergeometric distribution$ For large values of N the hypergeometric distribution may be approximated by the binomial distribution B(n, p), where p = w/N, since in this case sampling without replacement is approximately equivalent to sampling with replacement.
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