Exam MAS-I Practice Question 41

Study guide: Exam MAS-I

A book of business has two equally large classes of policy. In class 1, claim sizes are exponential with mean 100; in class 2, exponential with mean 1,000. Let X be the size of a claim from a policy chosen at random from the book, and let X_1 and X_2 be independent exponential random variables with means 100 and 1,000.

Determine which of the following statements are true.

• I. P(X > 500) = 0.5\,e^{-5} + 0.5\,e^{-0.5}

• II. \text{Var}(X) = 0.5\,(100^2) + 0.5\,(1{,}000^2)

• III. X has the same distribution as \tfrac{1}{2}X_1 + \tfrac{1}{2}X_2

• A) I only

• B) I and II only

• C) I and III only

• D) II and III only

• E) The answer is not given by (A), (B), (C), or (D)

Answer this question and see the worked solution

Concepts tested

• Mixture Distribution
• Exponential Distribution
• Variance for Conditional and Marginal Distributions
• Linear Combinations of Random Variables

More questions from this set

• Exam MAS-I Practice Question 40
• Exam MAS-I Practice Question 42