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Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance

This calculator calculates hypergeometric distribution pdf, cdf, mean and variance for given parameters

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of k successes in n draws with replacement. Wikipedia

Probability density function of the hypergeometric distribution is
f(k)=\frac{C^{K}_{k}C^{N-K}_{n-k}}{C^{N}_{n}},
where
C^{n}_{m}=\frac{n!}{m!(n-m)!} is the number of combinations of m from n or binomial coefficient

Cumulative distribution function of the hypergeometric distribution is
F(k)=1-{{{n \choose {k+1}}{{N-n} \choose {K-k-1}}} \over {N \choose K}}\,_{3}F_{2}\!\!\left[{\begin{array}{c}1,\ k+1-K,\ k+1-n\\k+2,\ N+k+2-K-n\end{array}};1\right],
where
_{p}F_{q} is the generalized hypergeometric function

Mean or expected value for the hypergeometric distribution is
\mu_k=n\frac{K}{N}

Variance is
\sigma^{2}_{k}=n\frac{K}{N}\frac{N-K}{N}\frac{N-n}{N-1}

The calculator below calculates the mean and variance of the negative binomial distribution and plots the probability density function and cumulative distribution function for given parameters n, K, N.

PLANETCALC, Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance

Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance

Digits after the decimal point: 2
Mean
0.6
Variance
0.46
Hypergeometric distribution
The file is very large. Browser slowdown may occur during loading and creation.
0123456789100.000.050.100.150.200.250.300.350.400.450.500.55

Hypergeometric distribution

Number of successesProbability of appearance
00.5041
10.3980
20.0918
30.0061
40
50
60
70
80
90
Items per page:
1 - 10 of 11
Cumulative distribution function
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0123456789100.500.550.600.650.700.750.800.850.900.951.00

Cumulative distribution function

Number of successesCumulative distribution function
00.5041
10.9020
20.9939
31
41
51
61
71
81
91
Items per page:
1 - 10 of 11

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