CAS Exam MAS-I Fall 2019, Question 18

Study guide: Exam MAS-I

You are given the following information about the distribution of losses:

• Losses follow an exponential distribution with mean \theta.
• Insurance payments for each loss are subject to a deductible of 500 and a maximum payment of 30,000:

\text{Insurance payment} = \min[30{,}000,\ \max(0,\ \text{loss} - 500)]

• No insurance payments are made for losses less than 500
• A random sample of five insurance payments are drawn:

1{,}000 \quad 4{,}900 \quad 7{,}000 \quad 19{,}500 \quad 30{,}000

Calculate the maximum likelihood estimate of \theta.

• A) Less than 12,500
• B) At least 12,500, but less than 13,500
• C) At least 13,500, but less than 14,500
• D) At least 14,500, but less than 15,500
• E) At least 15,500

Answer this question and see the worked solution

Concepts tested

• Maximum Likelihood Estimation
• Censoring
• Truncation
• Exponential Distribution
• Incomplete Data

More questions from this set

• CAS Exam MAS-I Fall 2019, Question 17
• CAS Exam MAS-I Fall 2019, Question 19