Exponential Distribution

The Exponential Distribution is a probability mass function that models a random variable in which small values occur more frequently than higher values.

Example

• The amount of change in someone’s pocket
• The number of mobile phones owned by a single person
• The total time spent in the gym per person

The exponential distribution is a special case of the gamma distribution, and the sum of exponential distributions produces such a distribution.

It is an example of a Memoryless Distribution.

---

Formula:

$Exp(x;\lambda )=\lambda e^{-\lambda x}$

Where

• $\lambda$ is the rate parameter

---

Cumulative Distribution Function

The cumulative distribution function for the exponential distribution is: $P(X\le k)=1-e^{-\lambda x}$

Properties

The mean of the exponential distribution can be calculated as: $\mu =\frac{1}{\lambda }$

The variance of the exponential distribution can be calculated as: $Var(x)=\frac{1}{{\lambda }^2}$