Random variable addition

If we have 2 independent variables, X and Y, with expectations E(X) and E(Y), and Var(X) and Var(Y):

E(X+Y)=E(X)+E(Y)

Var(X+Y)=Var(X)+Var(Y)

Standard deviation

As the standard deviation is the square root of the variance, to find \sigma of X+Y, we just find any of:

It’s the same as finding the hypotenuse of a right angle triangle. We need to square root the sum of squares.

Question	Answer
What happens to the expectations E(X+Y) when X and Y are independent variables?	E(X+Y) = E(X) + E(Y)
What happens to the variance Var(X+Y) when X and Y are independent variables?	Var(X+Y) = Var(X) + Var(Y)
How do you find the standard deviation \sigma of X+Y?	\sqrt{Var(X+Y)} or \sqrt{Var(X) + Var(Y)} or \sqrt{{\sigma_x}^2 + {\sigma_y}^2}
To what geometric concept is finding the standard deviation of X+Y similar?	Finding the hypotenuse of a right angle triangle, needing to square root the sum of squares.