CAS Exam MAS-II Fall 2019, Question 35
Study guide: Exam MAS-II
You assume that the number of claims for a single policy, Y, follows a Poisson distribution with mean parameter \lambda.
f(Y \mid \lambda) = \frac{e^{-\lambda}\lambda^{Y}}{Y!} \quad \text{for } Y \in \{0, 1, 2, 3, \ldots\}We initially choose an exponential prior for \lambda with mean 7. You find that the mean number of claims per policy in your dataset is 2, and the mode of the posterior distribution of \lambda is 2.1.
You are considering 3 possible alternative prior distributions.
I. Gamma with a mean of 7 and variance of 7 II. Exponential with a mean of 5 III. Uniform between 0 and 2
Determine which of the above alternative prior distributions will increase the mode (relative to the current mode) of the posterior distribution of \lambda.
- A) None
- B) I and II only
- C) I and III only
- D) II and III only
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution