Given a continuous random variable
with differential entropy
,
the entropy power of
is given by
We have the following two properties.
Property 1.77. Let
and
be independent continuous random variables of finite variance. Then the
differential entropy satisfies
![]() |
(1.14) |
with equality iff
and
are gaussian.
Property 1.78. Let
and
be two independent continuous vector valued random variables with finite
variance. Then