We know that the formula for Var(X + Y) is Var(X) + Var(Y) + 2Cov(X,Y)

Does this mean that for Var(X - Y) it is just:

Var(X) - Var(Y) - 2Cov(X,Y)?

Alan Smith
2022-01-14
Answered

What is Var(X - Y)?

We know that the formula for Var(X + Y) is Var(X) + Var(Y) + 2Cov(X,Y)

Does this mean that for Var(X - Y) it is just:

Var(X) - Var(Y) - 2Cov(X,Y)?

We know that the formula for Var(X + Y) is Var(X) + Var(Y) + 2Cov(X,Y)

Does this mean that for Var(X - Y) it is just:

Var(X) - Var(Y) - 2Cov(X,Y)?

You can still ask an expert for help

enhebrevz

Answered 2022-01-15
Author has **25** answers

The definition of variance.

Linearity of expectation:

Now note that:

Which immediately gives the result desired in terms of the covariance.

Marcus Herman

Answered 2022-01-16
Author has **41** answers

It will be Var(X)+Var(Y)−2Cov(X,Y), because Var(−Y)=Var(Y).

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