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.

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

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

• The probability of having 3 white marbles would be $f_X(3)=\frac{\left(\genfrac{}{}{0pt}{}{3+b-1}{3}\right)\left(\genfrac{}{}{0pt}{}{W+B-b-3}{W-3}\right)}{\left(\genfrac{}{}{0pt}{}{W+B}{W}\right)}=\frac{\left(\genfrac{}{}{0pt}{}{3+3-1}{3}\right)\left(\genfrac{}{}{0pt}{}{10+7-3-3}{10-3}\right)}{\left(\genfrac{}{}{0pt}{}{10+7}{10}\right)}=0.1697$

Title	negative hypergeometric random variable, example of
Canonical name	NegativeHypergeometricRandomVariableExampleOf
Date of creation	2013-03-22 12:39:04
Last modified on	2013-03-22 12:39:04
Owner	aparna (103)
Last modified by	aparna (103)
Numerical id	4
Author	aparna (103)
Entry type	Example
Classification	msc 62E15