Question

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

Answer 1

`"Var"(X+Y) = Var (X) + Var (Y) + 2"Cov" (X,Y)`

Explanation:

Note that

`"Var"(X+Y) = Var (X) + Var (Y) + 2"Cov" (X,Y)`

You can write

`"Var"(X+Y) = Var (X) + Var (Y)`

Only if `"Cov" (X,Y) = 0`