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I was trying to find an answer, but couldn't, what is the integral of the squared probability density function? It doesn't seem to be equal to the square of cumulative distribution function, but how to tackle it?

∫(f(x))^{2}dx = ? Can we transform it into, say, ∫f(x)dF(x)? and then ∫F'(x)dF(x) may be used somehow? I am not a mathematician so just throwing out some ideas I had, would appreciate any help with it :)

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# A Integral of squared univariate PDF

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