Say you have an iid random sample of size n from the following density: \"93) = {ozl + w)_'_1 if :c > 0 0 otherwise, Where oz > 0 and 3 > 0. For this question, assume that 3 is a known, xed value and therefore does not need to be estimated. (a) Find IE[X] (Note that it only exists when oz > 1). (b) Find the method of moments estimator for Oz. Is this a consistent estimator of oz? Justify your answer. (c) Find the maximum likelihood estimator of oz. (d) Derive a largesample 95% condence interval for the maximum likelihood estimator of oz