#### Exponential Distribution

Among probability distributions which are nonzero over a semi-infinite range of values and having a finite mean , the exponential distribution has maximum entropy.

To the previous case, we add the new constraint

 (D.39)

resulting in the objective function

Now the partials with respect to are

and is of the form . The unit-area and finite-mean constraints result in and , yielding

 (D.40)

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