I have a question about estimate the uncertainty of a function. I have a variable $x$. I assume that I can predict the variable $x$ is followed by a function $f(x)$ such as $$f(x)=\exp(-x^2)$$
Now, my goal is estimate level of perceptual uncertainty for that function $f(x)$ (because we don't know exactly function- just assume it, hence we must estimate the function). The natural way is that computes entropy function $$H(f)=-f\log_2(f)-(1-f)\log_2(1-f)$$
Is it correct for my goal? That mean to estimate the level of perceptual uncertainty of function $f$, We cannot consider any conditions and that equation is meaningful