Here is an example in which the bootstrapped centered sample mean in the parametric and empirical bootstrap simulations are the same. Consider the software data with average ¯xn = XXXXXXXXXXand median...

Here is an example in which the bootstrapped centered sample mean in the parametric and empirical bootstrap simulations are the same. Consider the software data with average ¯xn = 656.8815 and median mn = 290, modeled as a realization of a random sample X₁, X₂,...,X_n
from a distribution function F with expectation µ. By means of bootstrap simulation we like to get an impression of the distribution of
n − µ.

a. Suppose that we assume nothing about the distribution of the interfailure times. Describe the appropriate bootstrap simulation procedure with one thousand repetitions

b. Suppose we assume that F is the distribution function of an Exp(λ) distribution, where λ is estimated by 1/x¯n = 0.0015. Describe the appropriate bootstrap simulation procedure with one thousand repetitions.

 c. Suppose we assume that F is the distribution function of an Exp(λ) distribution, and that (as suggested by Exercise 18.6 a) the parameter λ is estimated by (ln 2)/mn = 0.0024. Describe the appropriate bootstrap simulation procedure with one thousand repetitions.