Hypergeometric Distribution: Difference between revisions
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Hypergeometric distribution counts the number of ways you can obtain particular target values when sampling from a population without replacement. | Hypergeometric distribution counts the number of ways you can obtain particular target values when sampling from a population without replacement. | ||
This describes many systems | This describes many systems - most notably a deck of 52 [[Cards]] (e.g. poker hands). | ||
Hypergeometric distribution: | Hypergeometric distribution: | ||
<math> | <math> | ||
\displaystyle{ | |||
\dfrac{ | \dfrac{ | ||
\binom{K}{k} \binom{N-K}{n-k} | \binom{K}{k} \binom{N-K}{n-k} | ||
}{ | }{ | ||
\binom{N}{n} | \binom{N}{n} | ||
} | |||
} | } | ||
</math> | </math> | ||
where: | |||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
K &=& \mbox{ | K &=& \mbox{Successes} \\ | ||
N &=& \mbox{ | N &=& \mbox{Pop. size} \\ | ||
k &=& \mbox{ | k &=& \mbox{Targets} \\ | ||
n &=& \mbox{Sample size} | n &=& \mbox{Sample size} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
==Flags== | |||
{{CombinatoricsFlag}} | |||
[[Category:Math]] | |||
Latest revision as of 21:34, 9 March 2019
Hypergeometric distribution counts the number of ways you can obtain particular target values when sampling from a population without replacement.
This describes many systems - most notably a deck of 52 Cards (e.g. poker hands).
Hypergeometric distribution:
$ \displaystyle{ \dfrac{ \binom{K}{k} \binom{N-K}{n-k} }{ \binom{N}{n} } } $
where:
$ \begin{align} K &=& \mbox{Successes} \\ N &=& \mbox{Pop. size} \\ k &=& \mbox{Targets} \\ n &=& \mbox{Sample size} \end{align} $
Flags
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Combinatorics
Combinatorial Structures - Order Does Not Matter Ordinary generating functions
Labelled Structures - Order Matters Enumerating Permutations: String Permutations Generating Permutations: Cool · Algorithm M (add-one) · Algorithm G (Gray binary code)
Combinatorics Problems Longest Increasing Subsequence · Maximum Value Contiguous Subsequence · Racing Gems Cards (poker hands with a deck of 52 playing cards)
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