In code: i(x) = x // We know i is uniformly distributed just as x is - preserve "unknowability" f(x) = x^2 // We know f has higher probability between [0,1] t

In code: i(x) = x // We know i is uniformly distributed just as x is - preserve "unknowability" f(x) = x^2 // We know f has higher probability between [0,1] than [1,2] g(x) = 1 // We know g is always 1. Just because your inputs are random, doesn't mean your output is - the implementation matters.