) The life of a module of a product follows an exponential distribution with an unknown parameter a. To make testing realistic, product items containing this module are put on life test. Three randomly selected items (Item 1, Item 2 and Item 3) of the product were put on test at time 0. Another randomly selected item (Item 4) was added to the test but at a later time s > 0. The life test was stopped at time T. Item 1 was withdrawn from test at x1 < T. Item 2 failed at x2 < T, and Item 3 failed at time x3 < T. Item 4 had not failed by T. Use the maximum likelihood estimation method to estimate the unknown parameter in the following steps. Part (a): (7 Points) Write down the likelihood function associated with the process of maximum likelihood estimation for this estimation problem with incomplete (or censored) data. Part (b): (5 Points) Derive the maximum likelihood estimator and express this estimator as a function of x1, x2, x3, x4, s and T Part (c): (3 Points) If one ignores items not having failed during the test, what would be the estimator for . Derive it or explain why. Part (d): (3 Points) Should you ignore life data about those items not having failed during the test. Explain your answer is up to two sentences. Part (e): (2 Points) In statistics, we always use sample mean and sample variance to estimate the unknown mean and variance. Since the mean is often referred to as the first moment of a distribution and the variance as the second moment, this method is often referred to as the method of moments. Why is it that this method is in general inadequate for estimating the unknown parameters of life distributions when censoring occurs?