Exam MAS-I Practice Question 35
Study guide: Exam MAS-I
Losses on a block of policies are uniformly distributed on (0, \theta). From a random sample of n = 5 losses, two unbiased estimators of \theta are proposed:
T_1: twice the sample mean,T_1 = 2\bar{X}T_2: the largest loss scaled up,T_2 = \tfrac{6}{5}X_{(5)}
You are given that, for a sample of size n from this distribution,
E\big[X_{(n)}\big] = \frac{n\theta}{n+1}, \qquad \text{Var}\big(X_{(n)}\big) = \frac{n\theta^2}{(n+1)^2(n+2)}Calculate the efficiency of T_2 relative to T_1, defined as \text{Var}(T_1)/\text{Var}(T_2).
- A) Less than 0.50
- B) At least 0.50, but less than 1.50
- C) At least 1.50, but less than 2.50
- D) At least 2.50, but less than 3.00
- E) At least 3.00
Answer this question and see the worked solution