An R Introduction to Statistics

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:

        1μe−x∕μ    when x ≥ 0
f(x) =  0         when x < 0

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



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.


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.

> pexp(2, rate=1/3) 
[1] 0.48658


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