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What do you call this function?
$$f(x) = x(1 - x)$$
Does it have a name? It’s cropped up in at least two statistical formulas I've been asked to program so far. (In both cases, $x$ was something called a $p$-value (for what it's worth).)
If Z can take values 1 or 0 with probability x and 1-x, respectively, we usually call x*(1-x) the variance of Z.
This is a special case of the more general variance formula, and works because Z is what we call an indicator variable.
Required, but never shown