Exam MAS-I Practice Question 10
Study guide: Exam MAS-I
An actuary has two years of claim counts for each of many insureds, and computes, per insured:
- mean count in one year: 0.20
- variance of a one-year count: 0.26
- variance of the two-year total count: 0.64
Three models are proposed. Each has a mean rate of 0.20 per year.
- Model I. Every insured's claims follow a Poisson process with rate 0.20.
- Model II. Each year, each insured's rate is drawn afresh, independently of the other year, from a distribution with mean 0.20 and variance 0.06. Given that year's rate, the year's count is Poisson.
- Model III. Each insured's rate is drawn once from a distribution with mean 0.20 and variance 0.06 and kept for both years: a mixed Poisson process.
Part a (1 point)
Under Model III, calculate the variance of an insured's two-year total count. Give your answer to two decimal places.
Part b (1 point)
Which model is consistent with all three statistics?
- A) Model I only
- B) Model II only
- C) Model III only
- D) Models II and III only
- E) Models I, II and III
Answer this question and see the worked solution
Concepts tested
- Mixed Poisson Process
- Mixing Distribution
- Poisson Process
- Variance for Conditional and Marginal Distributions
- Covariance