SOA Exam P Sample Question 169
Study guide: Exam P-1
An insurance company will cover losses incurred from tornadoes in a single calendar year. However, the insurer will only cover losses for a maximum of three separate tornadoes during this timeframe. Let X be the number of tornadoes that result in at least 50 million in losses, and let Y be the total number of tornadoes. The joint probability function for X and Y is
p(x,y) = \begin{cases} c(x+2y), & \text{for } x = 0,1,2,3,\ y = 0,1,2,3,\ x \le y \\ 0, & \text{otherwise,} \end{cases}where c is a constant.
Calculate the expected number of tornadoes that result in fewer than 50 million in losses.
- A) 0.19
- B) 0.28
- C) 0.76
- D) 1.00
- E) 1.10
Answer this question and see the worked solution