Question

How is entropy defined on a differential basis? (use an equation)?

Answer 1

Differential entropy differ's from the normal entropy as in case of differential entropy random variable needs not to be discrete.

The differential concept of entropy is as follows

Let X be a random variable which is continuous

Let
`f(x)` be it's probability distribution function

We have differential entropy h(X) defined as

`h(X)=-\int _(X)f(X)log[f(X)]dx`

The random variable 'X' need not to be discrete and it is continuous.