Statistics 320 Exam 3 Form A Fall 2015

Statistics 320 Exam 3 Form A

Fall 2015

· Write your name in the upper right (stapled) corner on the back of the test.

· Show your work. Clearly indicate your final answer.

· Carry out all calculations to at least 3 significant figures (unless they terminate sooner).

· You may use 1 sheet of notes, a calculator, and the tables in the back of the textbook.

· Numbers in brackets [ ] indicate how much a problem is worth.

1. [5] Find the 80th percentile of a binomial distribution with and .

2. [15] An observatory monitors a particular position in the sky and records the number of meteorites observed entering the atmosphere. During five (randomly selected) 2-hour time periods, they obtain the following data: 0, 0, 2, 2, and 4. Let X = the number of meteorites observed during a 2-hour period.

(a) [5] Find an unbiased estimate for .

(b) [5] Find an unbiased estimate for .

(c) [5] Assume that X has a Poisson distribution with and unknown. Based on your results above, find an unbiased estimate for = the average number of meteorites observed per hour.

3. [10] Suppose that X has a normal distribution with mean and variance . Let denote a random sample of size n taken from the distribution of X.

(a) [6] Find the method-of-moments estimator for . Express it in terms of .

(b) [4] Is the method-of-moments estimator for biased or unbiased? ____________________

If it is biased, does it tend to underestimate or overestimate ? ________________________

4. [15] Suppose that the density function for a random variable X is with

, , and unknown. Find the maximum likelihood estimator for , based on a random sample of size n.