10. Consider again the data in Table 3.1, also reproduced here for convenience (Table 5.7). These are the numbers of pump failures, Yi, observed in ti thousands of hours for k = 10 different systems of a certain nuclear power plant. The observations are listed in increasing order of raw failure rate ri, the classical point estimate of the true failure rate θi for the i

th system.

(a) Using the statistical model and results of the previous question, compute PEB point estimates and 90% equal-tail naive interval estimates for the true failure rates of systems 1, 5, 6, and 10.

(b) Using the approach of Laird and Louis (1987) and their Type III parametric bootstrap, obtain corrected 90% EBCIs for θ5 and θ6.

Why does the θ5 interval require more drastic correction?