Description
All of the following problems refer to the “Armadillo kills” data discussed in class. The data are
summarized in the table below for your convenience.
Kills Count
0 29
1 8
2 1
Use a Poi(λ) distribution to model the data, with λ being the unknown “kill rate.”
A. One or more of the following problems might be graded.
1. Estimate the kill rate using the method of Maximum Likelihood.
2. Estimate the standard error of the estimator in question 1 using Maximum Likelihood asymptotics.
3. Estimate the standard error of the estimator in question 1 using the Bootstrap.
4. Estimate the probability of at least one kill using the method of Maximum Likelihood.
5. Estimate the standard error of the estimator in question 4 using the delta method.
6. Estimate the standard error of the estimator in question 4 using the Bootstrap.
B. The following problem will be graded.
7. Compute Bayes estimate of the probability of at least one kill. Take the prior distribution to be
Gam(α0, β0), with β0 = 1.1 and α0 chosen so that the prior mean of λ is 0.25. Provide also a 95%
Credible Interval for the probability of at least one kill.
8. What would have been your answer to question 1 be, had the data consisted of 38 zeros? Compare
with the Bayesian answer and comment.
