negative hypergeometric random variable, example of
Suppose you have 7 black marbles and 10 white marbles in a jar. You pull marbles until you have 3 black marbles in your hand. $X$ would represent the number of white marbles in your hand.

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The expected value^{} of $X$ would be $E[X]=\frac{Wb}{B+1}=\frac{3(10)}{7+1}=3.75$

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The variance^{} of $X$ would be $Var[X]=\frac{Wb(Bb+1)(W+B+1)}{(B+2){(B+1)}^{2}}=\frac{10(3)(73+1)(10+7+1)}{(7+2){(7+1)}^{2}}=1.875$

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The probability of having 3 white marbles would be ${f}_{X}(3)=\frac{\left(\genfrac{}{}{0pt}{}{3+b1}{3}\right)\left(\genfrac{}{}{0pt}{}{W+Bb3}{W3}\right)}{\left(\genfrac{}{}{0pt}{}{W+B}{W}\right)}=\frac{\left(\genfrac{}{}{0pt}{}{3+31}{3}\right)\left(\genfrac{}{}{0pt}{}{10+733}{103}\right)}{\left(\genfrac{}{}{0pt}{}{10+7}{10}\right)}=0.1697$
Title  negative hypergeometric random variable, example of 

Canonical name  NegativeHypergeometricRandomVariableExampleOf 
Date of creation  20130322 12:39:04 
Last modified on  20130322 12:39:04 
Owner  aparna (103) 
Last modified by  aparna (103) 
Numerical id  4 
Author  aparna (103) 
Entry type  Example 
Classification  msc 62E15 