Problems: Assignment 5

- Page 362, Q 2.
- Page 362, Q 3.
- Page 369, Q44 b.
- Page 370, Q51 b,c.
- Suppose are independent
random variables. (This is the
usual set-up for the one-way layout.)
- Find the MLE's for and .
- Find the expectations and variances of these estimators.

- Find the MLE's for and .
- 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? - 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.

- 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- Find the likelihood equations for estimating and .
- Find the Fisher information matrix.

- Find the likelihood equations for estimating and .

Thu Oct 10 22:04:18 PDT 1996