4. Let Xi,..., Xn be a random sample with density 303 for 0 < θ < x NOTE: We have previously found that θMLE-X(1) and that FX(1) (x)-1-(!)3m (a) Using the probability integral transform method, find a pivot for 0 based on the MLE. (b) Use the pivot found in (a) to get an ezact 100(1-a)% C.1. for θ (c) Find an approximate 100(1-a)% C.1. for θ based on our result for the MLE. (d) Suppose that we get n = 100 samples from this distribution and we find that the MLE is 8, Calculate a 95% C.1. for using both methods (that from (b) and that from (c)). (e) Comment on the results obtained in (d). Which interval would you choose to report? Why? 4. Let Xi,..., Xn be a random sample with density 303 for 0