This works because the arithmetic mean of a large number of trials should converge to the "expected value", and expectation is linear: E(X+Y) = E(X)+E(Y). So th

This works because the arithmetic mean of a large number of trials should converge to the "expected value", and expectation is linear: E(X+Y) = E(X)+E(Y). So this can be a useful way to reason about sums of random variables.