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Hypergeometric Distribution: Definition, Properties and Application

 



Hypergeometric Distribution




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.



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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