Consider the software data, with average ¯xn = XXXXXXXXXX, modeled as a realization of a random sample X 1 , X 2 ,...,Xn from a distribution function F. We estimate the expectation µ of F by the...

Consider the software data, with average ¯xn = 656.8815, modeled as a realization of a random sample X₁, X₂,...,Xn from a distribution function F. We estimate the expectation µ of F by the sample mean and we are interested in the probability that the sample mean deviates more than ten from µ: P|X¯n − µ| > 10.

a. Suppose we assume nothing about the distribution of the interfailure times. Describe how one can obtain a bootstrap approximation for the probability, i.e., describe the appropriate bootstrap simulation procedure with one thousand repetitions and how the results of this simulation can be used to approximate the probability.

b. Suppose we assume that F is the distribution function of an Exp(λ) distribution. Describe how one can obtain a bootstrap approximation for the probability