Exam MAS-I Practice Question 1

Study guide: Exam MAS-I

Claims on a block of policies arrive as a Poisson process with a constant rate $\lambda$ per year, except where Part c says otherwise. Match each random quantity to the family of distributions it follows. An option may be used more than once or not at all.

Part a (1 point)

The time from the start of the year until the fourth claim.

A) Poisson
B) Exponential
C) Gamma
D) Uniform
E) Negative binomial

Part b (1 point)

The number of claims in the first half of the year that exceed a deductible, when each claim exceeds it with probability 0.3, independently of the arrival process and of the other claims.

A) Poisson
B) Exponential
C) Gamma
D) Uniform
E) Negative binomial

Part c (1 point)

The number of claims next year for a policyholder chosen at random from a portfolio in which each policyholder has its own fixed rate, and those rates follow a gamma distribution across the portfolio.

A) Poisson
B) Exponential
C) Gamma
D) Uniform
E) Negative binomial

Part d (1 point)

The time from now until the next claim, given that the most recent claim occurred two months ago.

A) Poisson
B) Exponential
C) Gamma
D) Uniform
E) Negative binomial

Part e (1 point)

Given that exactly one claim occurred during the year, the time within the year at which it occurred.

A) Poisson
B) Exponential
C) Gamma
D) Uniform
E) Negative binomial

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