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.
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?
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.
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.