[acchow]

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.

[dmd]

... which is exactly what I said. What are you adding here?