# An Alternative Variance Formula

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## Summary:

Interesting formula for variance

## Main Question or Discussion Point

I derived (trivially) an expression for the variance of a random variable (which I had never noticed before). Let ##X## be a random variable with cdf ##F(x)## then (assuming finite second moment). ##Var(X)=\frac{1}{2}\int\int (x-y)^2dF(x)dF(y)##.

Is this expression of any use?

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It looks so much more complicated than other equations that I can't think of a use for it.
This seems much more convenient: ##Var(X) = \int {X^2}dF - (\int X dF)^2##

PS. I have not taken time to verify your formula. I do not see it immediately.