#### STAT 450

Problems: Assignment 5

1. Page 362, Q 2.

2. Page 362, Q 3.

3. Page 369, Q44 b.

4. Page 370, Q51 b,c.

5. Suppose are independent random variables. (This is the usual set-up for the one-way layout.)

1. Find the MLE's for and .

2. Find the expectations and variances of these estimators.

6. In the previous question take for all i and let . What happens to the MLE of ? Hint: you have calculated the mean and variance of the MLE of . What are the limits of these quantities?

7. Suppose that are independent random variables and that are the corresponding values of some covariate. Suppose that the density of is

where , and are unknown parameters. Find the log-likelihood, the score function and the Fisher information.

8. For each of the doses a number of animals are treated with the corresponding dose of some drug. The number dying at dose d is Binomial with parameter . A common model for is

1. Find the likelihood equations for estimating and .

2. Find the Fisher information matrix.

Richard Lockhart
Thu Oct 10 22:04:18 PDT 1996