Question

How do you calculate the standard deviation of a bounded probability distribution function?

Answer 1

`sqrt( int_a^b x^2*f(x) dx - (int_a^b xf(x) dx)^2)`

Explanation:

Bounded or not use expectation, assume the following PDF
`f(x), a < x < b`

then the expectation for standard deviation is calculated as

`sqrt(VAR(x)) =sqrt(E(x^2) - E(x)^2) =`
`sqrt( int_a^b x^2*f(x) dx - (int_a^b xf(x) dx)^2)`