# For random variables X and Y. What is "Var"(X+Y) in terms of "Var"(X) and Var(Y)?

Oct 29, 2015

$\text{Var"(X+Y) = Var (X) + Var (Y) + 2"Cov} \left(X , Y\right)$

#### Explanation:

Note that

$\text{Var"(X+Y) = Var (X) + Var (Y) + 2"Cov} \left(X , Y\right)$

You can write

$\text{Var} \left(X + Y\right) = V a r \left(X\right) + V a r \left(Y\right)$

Only if $\text{Cov} \left(X , Y\right) = 0$