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