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) |
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) |