# 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 $Var[X]=\frac{Wb(B-b+1)(W+B+1)}{(B+2)(B+1)^{2}}=\frac{10(3)(7-3+1)(10+7+1)}{(7+% 2)(7+1)^{2}}=1.875$

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The probability of having 3 white marbles would be $f_{X}(3)=\frac{{3+b-1\choose 3}{W+B-b-3\choose W-3}}{{W+B\choose W}}=\frac{{3+% 3-1\choose 3}{10+7-3-3\choose 10-3}}{{10+7\choose 10}}=0.1697$

Title negative hypergeometric random variable, example of NegativeHypergeometricRandomVariableExampleOf 2013-03-22 12:39:04 2013-03-22 12:39:04 aparna (103) aparna (103) 4 aparna (103) Example msc 62E15