Variance question: If V (Y) = 6, then V (2Y- 4) =

Question

If V (Y) = 6, then V (2Y- 4) =

Answer 1

Var(aX + b) = a²Var(X)

Adding or subtracting values does not change the variance.

Therefore, if Var(Y) = 6, then Var(2Y - 4) = 2²Var(Y) = 4*6 = 24

Answer 2

We use two properties of variance:

1. Var(kX)=k^2Var(X)
2. Var(X+c)=Var(X)

By the second property, Var(2Y - 4)=Var(2Y)

By the first property Var(2Y)=2^2Var(Y)

Since Var(Y)=6, we have Var(2Y - 4)=2^2*6=24