. 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.
7. 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.
8. What would have been your answer to question 1 be, had the data consisted of 38 zeros? Comparewith the Bayesian answer and comment.
