Question

9. Suppose Var(X] = 4, Var[Y-1, and Cov(X, Y] =-1. Calculate VarX-2Y + 101.

Answer 1

Given :-

Var(X)= 4,

Var(Y) = 1,

Cov(X,Y) = -1

Now we have to find Var(X-2Y+10)

Therefore,

Var(X-2Y+10) = Var (X) - Var(2Y) + Var(10)

For variance property, any variance of any constant value is equal to zero.

Here 10 is constant value. So Var(10)=0

Var(X-2Y+10) = Var(X) + 4Var(Y) - 0

= Var(X) + 4Var(Y) + 2Cov(X, -2Y) ----- using formula

= Var(X) + 4Var(Y) - 4Cov(X, Y)

= 4 + 4*1 - 4*(-1)

Var(X-2Y+10) = 12