# 2.9 The Exponential Distribution

The *exponential distribution*, also called the negative exponential distribution, is used in dealing with queuing problems. The exponential distribution often describes the time required to service a customer. The exponential distribution is a continuous distribution. Its probability function is given by

where

$X=\text{randomvariable}\left(\text{servicetimes}\right)$

$\mu =\text{averagenumberofunitstheservicefacilitycanhandleinaspecificperiodoftime}$

$\text{e}=2.718\text{}\left(\text{thebaseofthenaturallogarithm}\right)$

The general shape of the exponential distribution is shown in Figure 2.16. Its expected value and variance can be shown to be

As with any other continuous ...

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