# Exponential Distribution

The exponential distribution describes the arrival time of a randomly recurring independent event sequence. If μ is the mean waiting time for the next event recurrence, its probability density function is:

Here is a graph of the exponential distribution with μ = 1.

#### Problem

Suppose the mean checkout time of a supermarket cashier is three minutes. Find the probability of a customer checkout being completed by the cashier in less than two minutes.

#### Solution

The checkout processing rate is equals to one divided by the mean checkout completion time. Hence the processing rate is 1/3 checkouts per minute. We then apply the function pexp of the exponential distribution with rate=1/3.

#### Answer

The probability of finishing a checkout in under two minutes by the cashier is 48.7%