Question

Suppose the standard deviation of X is 4 and the standard deviation of Y is 3. Answer the following two questions.

What is Var[7X + 2Y] if the covariance of X and Y is 10?

What is Var[7X + 2Y] if X and Y are independent?

Answer 1

Formula to use:

Hence, 1240 is Var(7x+2y).

b) When x and y are independent then covariance = 0

Hence, V(7x+2y) = 820 when X and Y are independent.

Please comment if any doubt. Thank you.