Question: LetX andY be random variables with finite expected values and variances. 1. If Var(X + Y) = Var(X) + Var(Y) then X and Y are

LetX andY be random variables with finite expected values and variances.

1. If Var(X + Y) = Var(X) + Var(Y) then X and Y are independent

2. If X and Y are independent then Var(X + Y) = Var(X) + Var(Y)

3. If Var(X + Y) = Var(X) + Var(Y) then Cov(X, Y) = 0

4. If Cov(X, Y) = 0, then Var(X + Y) = Var(X) + Var(Y)

Are those four statements all correct?

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