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

1 Answer
Will
Sep 2, 2016

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)

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