Twenty motors were put on test under a high-temperature setting. The lifetimes in hours of the motors under these conditions are given below. Also, the data are in the file lifetimemotor.rda at the site listed in the Preface. Suppose we assume that the lifetime of a motor under these conditions, X, has a Γ(1, θ) distribution.
(a) Obtain a histogram of the data and overlay it with a density estimate, using the code hist(x,pr=T); lines(density(x)) where the R vector x contains the data. Based on this plot, do you think that the Γ(1, θ) model is credible?
(b) Assuming a Γ(1, θ) model, obtain the maximum likelihood estimate θ 9 of θ and locate it on your histogram. Next overlay the pdf of a Γ(1, θ 9) distribution on the histogram. Use the R function 
to evaluate the pdf.
(c) Obtain the sample median of the data, which is an estimate of the median lifetime of a motor. What parameter is it estimating (i.e., determine the median of X)? (d) Based on the mle, what is another estimate