Given Problem -

Let X1, X2, .. . Xn be a random sample from a distribution with the following pdf: a . 2a f(xi ) Xi .a+1 Xi > 2 0 elsewhere Here, the expected value is za and the parameter of interest is a. a.) Find the method of moments estimator for a. (5pts.) b.) Find the maximum likelihood estimator for a. (5pts.)o} Using the following data, what is the method of moments estimate for :1? {Bots} x1 = 2.91 x: = 2.34 H3 = 2.3? in = 2.04 15 = it]? x: = 2.14 ills = 3.13 IQ = 2.5 d.] Using the data above, what is the maximum likelihood estimate for d? {3pm.} e.',l What is the maximum likelihood estimator and estimate for e'rz? {dots} its. = 2.4? H11} = 2.49