Question

Consider the following linear combination: Z = 4X - 5Y with E(X) = 3.2, V(X) = 1.3, E(Y) = 4.6, V(Y) = 5.1, and Cov (X, Y) = 0. What is the correct value of E(Z)? A. -20.3 B. -10.2 C. -6.7 D. 10.2 E. 20.3

Answer 1

Option B.

Explanation:

The given values are

E(X) = 3.2, V(X) = 1.3, E(Y) = 4.6, V(Y) = 5.1, and Cov (X, Y) = 0.

The given linear combination is

`Z=4X-5Y`

Now,

`E(Z)=E(4X-5Y)`

It can be written as

`E(Z)=4E(X)-5E(Y)`

Now, substitute the given values.

`E(Z)=4(3.2)-5(4.6)`

`E(Z)=12.8-23`

`E(Z)=-10.2`

Therefore, the correct option is B.