The Hypergeometric distribution is a type of statistical distribution that can be used to calculate various statistical measures such as mean, standard deviation, variance, etc. This distribution is a result of a hypergeometric random variable.
Where,
N: Total number of items in the population.
n: Total number of items in the sample.
x: Number of items in the sample that are considered successes.
P(x| N, n, k): This represents the hypergeometric probability, which is the probability of getting exactly x successes in an n-trial hypergeometric experiment, when the population consists of N items, k of which are considered successes.
Illustrative Examples
Example 1: What is the probability density function of the hypergeometric function for N=60, n=15, and m=8?
Solution:
Given parameters are,
N = 60
n = 15
m = 8
The hypergeometric distribution formula is:
P(x|N,m,n) =
Substituting the values, we get:
P(x|60, 8, 15) =