I do not know why you are simulating this system. Given random x, y, controlling for z = x + y trivially generates a perfect anticorrelation as x = z – y. Lik

I do not know why you are simulating this system. Given random x, y, controlling for z = x + y trivially generates a perfect anticorrelation as x = z – y. Like, I get that you want to make a point, just seems weird to have a numerical solution in 5 lines of code to a problem that was already theoretically solved when you wrote down the problem statement and therefore required exactly 0 equations...? Also like the theoretical solution clarifies that this happens for arbitrary probability distributions equally, it is not specific to Bernoulli random variables.