CAS Exam MAS-I Fall 2018, Question 25
Study guide: Exam MAS-I
You draw a large number of independent samples, each of size n = 4, from a uniform distribution on (0, \theta). You want to use the second smallest value in each sample as an estimate for the mean.
The density for the k^{\text{th}} order statistic of a sample is given as:
g_k(y_k) = \frac{n!}{(k-1)!(n-k)!}[F(y_k)]^{k-1}[1 - F(y_k)]^{n-k} f(y_k)
Calculate the expected bias of this estimate.
- A)
-\dfrac{4\theta}{5} - B)
-\dfrac{4\theta}{7} - C)
-\dfrac{\theta}{10} - D)
-\dfrac{\theta}{30} - E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution