CAS Exam MAS-I Spring 2019, Question 15

Study guide: Exam MAS-I

You are given the following information:

• x_1, x_2, \ldots, x_{500} is a random sample of 500 claims
• The distribution function is F(x) = 1 - \left(\frac{200}{x}\right)^{\alpha}; for x > 200 and \alpha > 0
• \sum_{i=1}^{500} x_i = 117{,}378{,}845 and \sum_{i=1}^{500} \ln(x_i) = 3{,}646
• The parameter \alpha is estimated using the method of maximum likelihood

Calculate the estimated probability that a claim will exceed 400.

• A) Less than 0.2
• B) At least 0.2, but less than 0.4
• C) At least 0.4, but less than 0.6
• D) At least 0.6, but less than 0.8
• E) At least 0.8

Answer this question and see the worked solution

Concepts tested

• Maximum Likelihood Estimation
• Single-Parameter Pareto Distribution
• Cumulative Distribution Function (CDF)
• Probability Density Function (PDF)

More questions from this set

• CAS Exam MAS-I Spring 2019, Question 14
• CAS Exam MAS-I Spring 2019, Question 16