6.4.3. The Hypergeometric Probability Distribution

Example 7:

Suppose there are 50 officers, 10 female officers and 40 male officers. Suppose 20 of them

will be promoted. Let X represent the number of female promotions. Then,

Therefore, the probability distribution function for X is

Hypergeometric Probability Distribution:

There are N elements in the population, r elements in group 1 and the other N-r elements

in group 2. Suppose we select n elements from the two groups and the random variable X

represent the number of elements selected from group 1. Then, the probability distribution

function for X is

Note: is the number of combinations as selecting i elements from group 1 while

is the number of combinations as selecting n-i elements from group2.

is the total number of combinations as selecting n elements from the two groups

while is the total number of combinations as selecting i and n-i elements

from groups 1 and 2, respectively.

JavaStatSoft:

Probability density:

Statistics -> Probability -> Probability Functions -> Probability Density Function (PDF)

Probability density:

Statistics -> Probability -> Probability Functions -> Cumulative Distribution Function (CDF)

Percentile (or Quantile):

Statistics -> Probability -> Probability Functions -> Percentile Function