Exam MAS-I Practice Question 37
Study guide: Exam MAS-I
For a portfolio, the number of claims N in a year has a negative binomial distribution with r = 2 and \beta = 1.5, so that E[N] = r\beta and \text{Var}(N) = r\beta(1 + \beta). Claim amounts X_1, X_2, \ldots are independent, exponentially distributed with mean 500, and independent of N. Aggregate losses are S = X_1 + \cdots + X_N.
Calculate \text{Cov}(N, S).
- A) 0
- B) 1,500
- C) 3,750
- D) 8,250
- E) 1,875,000
Answer this question and see the worked solution
Concepts tested
- Covariance
- Aggregate Loss Model
- Negative Binomial Distribution
- Exponential Distribution
- Expected Value