SOA Exam P Sample Question 89
Study guide: Exam P-1
Let N_1 and N_2 represent the numbers of claims submitted to a life insurance company in April and May, respectively. The joint probability function of N_1 and N_2 is
p(n_1, n_2) = \begin{cases} \frac{3}{4} \left(\frac{1}{4}\right)^{n_1-1} e^{-n_1} (1 - e^{-n_1})^{n_2-1}, & n_1=1,2,3,\dots \text{ and } n_2=1,2,3,\dots \\ 0, & \text{otherwise.} \end{cases}
Calculate the expected number of claims that will be submitted to the company in May, given that exactly 2 claims were submitted in April.
- A)
\frac{3}{16}(e^2-1) - B)
\frac{3}{16}e^2 - C)
\frac{3e}{4-e} - D)
e^2-1 - E)
e^2
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