CAS Exam MAS-II Fall 2019, Question 27

Study guide: Exam MAS-II

When modeling claim frequency, an actuary chooses to use the following Bayesian model:

\begin{align*}
Y &\sim \text{Poisson}(\mu) \\
\mu &\sim \text{Gamma}(\alpha = 1,\ \theta = 0.1)
\end{align*}

Suppose the actuary observed 10 claims from 250 policies in the past year.

Calculate the mean of the posterior predictive distribution for 250 policies.

• A) Less than 5
• B) Greater than or equal to 5 but less than 10
• C) Greater than or equal to 10 but less than 15
• D) Greater than or equal to 15 but less than 20
• E) Greater than or equal to 20

Answer this question and see the worked solution

Concepts tested

• Predictive Distribution
• Conjugate Prior
• Bayesian Credibility
• Gamma
• Posterior Distribution

More questions from this set

• CAS Exam MAS-II Fall 2019, Question 26
• CAS Exam MAS-II Fall 2019, Question 28