MA2102

Probability and Statistics

Lecture-18

Exponential Distribution:

A $Gamma(1,\lambda)$ distribution is called an Exponential distribution.

If$X\sim Gamma(1,\lambda)$ then $PDF$ of $X$, $f_X(x)=\left\{\begin{matrix} \lambda e^{-\lambda x}& x>0 \\ 0& x\le 0 \end{matrix}\right.$, and $CDF$ of $X$, $F_X(x)=\left\{\begin{matrix} 0&x\le 0 \\ 1-e^{-\lambda x}& x>0 \end{matrix}\right.$

Notation: $X\sim Exp(\lambda)$