試題詳解

80. Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which
E(X)=5, E(X²)=27.4,E(Y)=7,E(Y²)=51.4,Var(X+Y)=8.
Let C₁=X+Y denote the size of the combined claims before the application of a 20% surcharge on the hospital portion of the claim, and let C₂ denote the size of the combined claims after the application of that surcharge.
Calculate Cov(C₁,C₂) .
(A) 8.80
(B) 9.60
(C) 9.76
(D) 11.52
(E) 12.32