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:

• \sqrt{Var(X+Y)}
• \sqrt{Var(X)+Var(Y)}
• \sqrt{{\sigma_x}^2+{\sigma_y}^2}

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