Question

Let X, Y, and Z be random variables, and let Cov(⋅,⋅) denote the covariance operator as usual. Suppose that the variance of X is 0.7, Cov(X,Y) = 0.4, Cov(X,Z) = 1.2, and Cov(Y,Z) = 0.8. Find each of the following to two decimal places.

(a) Cov(5Y, 6X)
a) 4.80
(b) Cov(5Y + 3, 6X + 8Z)
a) 50.40

Answer 1

The covariance between 5Y and 6X is 12, and the covariance between 5Y + 3 and 6X + 8Z is 87.6.

Step-by-step explanation:

Given the information provided, we can calculate the covariance using the formula: Cov(aX, bY) = abCov(X, Y).

For part (a), Cov(5Y, 6X) = (5)(6)(0.4) = 12. For part (b), Cov(5Y + 3, 6X + 8Z) = (5)(6)(0.4) + (6)(8)(1.2) = 30 + 57.6 = 87.6.

Therefore, to two decimal places, Cov(5Y, 6X) = 12 and Cov(5Y + 3, 6X + 8Z) = 87.6.