Exponential Distribution

$X$ is said to have an exponential distribution with parameter $λ > 0$ if the PDF of $X$ is:

f (x; λ) = λ e^{- λ x}

where $x > 0$ .

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CDF for Exponential Distribution

Let $X$ has an exponential distribution with parameter $λ$ . Then the CDF of $X$ is:

F (x; λ) = {\begin{cases} 0 & x \leq 0 \\ 1 - e^{- λ x} & x > 0 \end{cases}

The mean and standard deviation of $X$ are both $\frac{1}{λ}$ .