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.”
- One or more of the following problems might be graded.
- Estimate the kill rate using the method of Maximum Likelihood.
- Estimate the standard error of the estimator in question 1 using Maximum Likelihood asymptotics.
- Estimate the standard error of the estimator in question 1 using the Bootstrap.
- Estimate the probability of at least one kill using the method of Maximum Likelihood.
- Estimate the standard error of the estimator in question 4 using the delta method.
- Estimate the standard error of the estimator in question 4 using the Bootstrap.B. The following problem will be graded.
- Compute Bayes estimate of the probability of at least one kill. Take the prior distribution to beGam(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.
- What would have been your answer to question 1 be, had the data consisted of 38 zeros? Comparewith the Bayesian answer and comment.
