MA2102

Probability and Statistics

Lecture-17(Part-a)

Hyper Geometric Distribution:

Suppose a population consist of $N$ items in which $M$ are type-I and remaining $N-M$ are type-II. $n$ items are drawn at random from the population without replacement. Let $X$ denote the number of items of type-I in the selection.

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

$PMF:$ $p_X(x)=P(X=x)=\frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}}$, $x\in S_X$