SOA Exam P Sample Question 242
Study guide: Exam P-1
Let X denote the loss amount sustained by an insurance company’s policyholder in an auto collision. Let Z denote the portion of X that the insurance company will have to pay. An actuary determines that X and Z are independent with respective density and probability functions
f(x)=\begin{cases}(1/8)e^{-x/8}, & x>0\\ 0, & \text{otherwise}\end{cases}and
P[Z=z]=\begin{cases}0.45, & z=1\\ 0.55, & z=0.\end{cases}Calculate the variance of the insurance company’s claim payment ZX.
- A) 13.0
- B) 15.8
- C) 28.8
- D) 35.2
- E) 44.6
Answer this question and see the worked solution