stat questions:

Exercise E10.3 (Methods of Moments Estimate for Continuous Uniform Distribution (6 points)) Consider a continuous uniform distribution on [a, b]. f(x) = b - a if x E [a, b] 0 otherwise Now you are given a dataset of n IID samples. The first moments are E(X) = (a + b)/2 and E(X2) = (a2 + 62 + ab)/3. (a) Give an MM estimator, based on lower non-central moments, for parameters a and b. (b) Now let the sample set S = {2, 3, 4, 5, 18}. Compute the MM estimate. Is the result plausible