Twenty motors were put on test under a high-temperature setting. The lifetimes in hours of the motors under these conditions are given below. Suppose we assume that the lifetime of a motor under these conditions, X, has a Γ(1, θ) distribution.

(a) Obtain a frequency distribution and a histogram or a stem-leaf plot of the data. Use the intervals [0, 50), [50, 100), . . . . Based on this plot, do you think that the Γ(1, θ) model is credible?

(b) Obtain the maximum likelihood estimate of θ and locate it on your plot.

(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 of the median of X?

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