I am not a statistician, but am working a proof for the upper bound of an expression which contains the variance of a variable which obtains its values from a closed interval, [0,1]. I have seen in several places (mostly forums and web pages) the result that $\text{Var}(X)\le \frac{(b-a)^2}{4}$ for $a\le X\le b$. I would like to use, and cite, this result but am having an unusually difficult time finding a solid reference. Could someone here recommend one for me?
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