Hypergeometric Distribution: Definition, Properties and Applications

 



Hypergeometric Distribution


hypergeometric distribution by statisticalaid.com


A discrete random variable X is said to have a  hypergeometric distribution if its probability density function is defined as,
 


where N is a positive integer , M is a non-negative integer that is at most N and n is the positive integer that at most M. If any distribution function is defined by the following probability function then the distribution is called hypergeometric distribution.


hypergeometric distribution plot


Properties of Hypergeometric Distribution

  • Hypergeometric distribution tends to binomial distribution if N➝∞ and K/N⟶p.
  • Hypergeometric distribution is symmetric if p=1/2; positively skewed if p<1/2; negatively skewed if p>1/2.
  • The mean of the hypergeometric distribution concides with the mean of the binomial distribution if M/N=p.

 Mean

 

 Variance

 

CF

 

 MGF

 

 

 





 Application of Hypergeometric Distribution

  • The hypergeometric distribution is commonly studied in most introductory probability courses. In introducing students to the hypergeometric distribution, drawing balls from an urn or selecting playing cards from a deck of cards are often discussed. This is a simple process which focus on sampling without replacement. 
  • We are also used hypergeometric distribution to estimate the number of fishes in a lake.

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