SOA Exam P Sample Question 628
Study guide: Exam P-1
In a given month, a group of policies are up for renewal. The random variable R denotes the fraction of those policies that are actually renewed. R has a probability density function of the form
f(r) = \begin{cases}
(\alpha + 1)r^\alpha, & \text{for } 0 < r < 1 \\
0, & \text{otherwise,}
\end{cases}where \alpha is a positive parameter. The expected value of R is 0.75.
Calculate the probability that more than half of the policies up for renewal in a given month will actually be renewed.
- A)
0.50 - B)
0.58 - C)
0.70 - D)
0.75 - E)
0.88
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