Actuarial Notes

CAS Exam MAS-II Spring 2019, Question 20

Study guide: Exam MAS-II

You are analyzing the claim counts for n individual policyholders. Let Y_i denote the claim count for the i^{th} policyholder. You build your model as follows:

\Pr(Y_i = y_i \mid P = p) = (1-p)^{y_i}p
f(p) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}p^{\alpha-1}(1-p)^{\beta-1}
f(\alpha) = \frac{1}{5}e^{-\alpha/5}
f(\beta) = \frac{1}{8}e^{-\beta/8}

Assuming that p is constrained to be between 0 and 1, the conditional posterior distribution of p \mid (\alpha, \beta, y_1, \ldots, y_n) is proportional to K.

Identify which of the following could be K.

  • A) p^{\alpha-1}(1-p)^{\beta-1}
  • B) p^{\alpha}(1-p)^{y_i+\beta-1}
  • C) \frac{\beta}{8}\frac{\alpha}{5}p^{\alpha+n-1}(1-p)^{\sum y_i+\beta-1}
  • D) p^{4+n}(1-p)^{\sum y_i+7}
  • E) None of the above could be K.

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