Exponential Distribution

The exponential distribution is a continuous distribution that runs on a single parameter, lambda. The probability density function (PDF) of this distribution is given by

f(x) = \lambda e^{-\lambda x}, \text{ } \lambda > 0

What does the PDF look like? We use the R code dexp for that. Following is the PDF of an exponential distribution function with parameter lambda = 0.01.

The cumulative distribution of exponential distribution is given by

F(x) = 1- e^{-\lambda x}

Mean and variance of exponential distribution

The expected value (mean) and variance of the distribution is given by

\\ E(X) = \frac{1}{\lambda} \\ \\ var(X) = \frac{1}{\lambda^2}

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