Can think of standard deviation much like a distance. So, if have random variables X and Y, if they have finite means and standard deviations, and if we denote

Can think of standard deviation much like a distance. So, if have random variables X and Y, if they have finite means and standard deviations, and if we denote standard deviation by Std(X) and variance by Var(X) and set Z = X + Y, then Var(X) = Std(X)^2 and we get the Pythagorean theorem Var(Z) = Var(X + Y) = Var(X) + Var(Y) if we can assume that X and Y are uncorrelated which is true if X and Y are independent. So, uncorrelated is analogous to perpendicular in geometry.