Fair enough. So, in the world beyond B-level, if I have an independent variable x ∈ A and a function f(x) = ## \frac 1 { \sqrt { 2 \pi }} e ^ { - \frac { x^2 } 2 } ##, and I have another variable y ∈ B and a second function g(y) = ## \frac 1 { \sqrt { 2 \pi }} e ^ { - \frac { y^2 } 2 } ##, if I don't attach some human interpretation to the variables and formulas, how would I know if f(x) is a random function ( that for example expresses a normal probability distribution for the number of customers in a shop based on the amount of rain), and g(y) is a regular explicit formula ( that for example describes the exact, non-random, number of items some clockwork machine will build in 1 hour based on the hardness of the raw materials fed to it)?As is often the case, I look to Feller volume 1 for inspiration.

which directly contradicts this:

The issue is: I don't think there is a satisfyingBlevel answer to this thread.

That is, what are the mathematical qualities of the domains A and B (or the functions f(x) and g(x)) that make one related to "random" and "probability" and the other just another explicit formula?

Last edited: