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Example There are N_{1} white balls and N_{2} black balls in the jar. Let X be the number of white balls when taking out n balls one by one without undoing (non-restoration extraction). Find the probability that the number of white balls is i Answer Note that

P_{r}(X = i) = \begin{matrix}\binom{N_{1}}{i} & \binom{N_{2}}{n−i} \\ ( & {N \atop n} & ) \end{matrix}

Random variable X follows a hypergeometric distribution and we write

X ∼ H_{g}(N, N_{1}, n)

Also,

E(X) = \frac{nN_{1}}{N} , V (X) = \frac{nN_{1}}{N} · \frac{n − N_{1}}{N} · \frac{N − n}{N − 1}