試題詳解

284. An employer provides disability benefits to its employees for work-related and other injuries. The random variables X and Y denote the employer’s annual expenditures for work-related and other injuries, respectively. An actuarial study reveals the following information about X and Y:
i) The density of X is , for x＞0
ii) Var (Y) = 12,500.
iii) The correlation between X and Y is 0.20.
Calculate the variance of the employer’s total expenditures for work-related and other injuries.
(A) 12,500
(B) 13,500
(C) 15,500
(D) 16,500
(E) 18,972