Sums and Differences of Random Variables
Suppose X and Y are independent random variables. Then, the variance of (X + Y) and the variance of (X - Y) are described by the following equations
Var(X + Y) = Var(X) + Var(Y)
Var(X - Y) = Var(X)- Var(Y)
Note: The standard deviation (SD) is always equal to the square root of the variance (Var). Thus,
SD(X + Y) = sqrt[ Var(X + Y) ]
and
SD(X - Y) = sqrt[ Var(X - Y) ]
where Var(X + Y) is the variance of the sum of X and Y, Var(X - Y) is the variance of the difference between X and Y, Var(X) is the variance of X, and Var(Y) is the variance of Y.
value of Var(X + Y) or var (X-Y) be A and var(x) be X and var(y) Y
