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Probability and Statistics


Hyper Geometric Distribution:

Suppose a population consist of NN items in which MM are type-I and remaining NMN-M are type-II. nn items are drawn at random from the population without replacement. Let XX denote the number of items of type-I in the selection.

SX={x:x is an integer and max(0,n(NM))xmin(M,n)}S_X=\{x:x\text{ is an integer and } max(0,n-(N-M))\le x \le min(M,n)\}

PMF:PMF: pX(x)=P(X=x)=(Mx)(NMnx)(Nn)p_X(x)=P(X=x)=\frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}}, xSXx\in S_X