Exam MAS-I Practice Question 65

Study guide: Exam MAS-I

An actuary has 40 individual claim amounts, all fully observed, and estimates F(1{,}000) = P(X \le 1{,}000) by the empirical distribution function, obtaining F_{40}(1{,}000) = 0.30.

Which statement about this estimate is correct?

• A) The number of claims at or below 1,000 is binomial, so the estimate is unbiased
• B) Its variance is estimated by 0.30 × 0.70 / 39, as one degree of freedom is used up
• C) Its standard error would be cut in half if the number of claims were doubled to 80
• D) It is biased low, because the step function F_{40} lies below F between data points
• E) The same claims would estimate F more precisely at their median than at 1,000

Answer this question and see the worked solution

Concepts tested

• Empirical Distribution
• Binomial Distribution
• Unbiasedness

More questions from this set

• Exam MAS-I Practice Question 64
• Exam MAS-I Practice Question 66