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Probability and Statistics


Exponential Distribution:

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

IfXGamma(1,λ)X\sim Gamma(1,\lambda) then PDFPDF of XX, fX(x)={λeλxx>00x0f_X(x)=\left\{\begin{matrix} \lambda e^{-\lambda x}& x>0 \\ 0& x\le 0 \end{matrix}\right., and CDFCDF of XX, FX(x)={0x01eλxx>0F_X(x)=\left\{\begin{matrix} 0&x\le 0 \\ 1-e^{-\lambda x}& x>0 \end{matrix}\right.

Notation: XExp(λ)X\sim Exp(\lambda)