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3. (14 points) Let X1, X2, . . . X\" be random sample from a distribution with probability density function f(:1:|a) = 40:03875'34, :1: > 0, o: > 0 (a) (10 points) Obtain the maximum likelihood estimator of a, it. (a) (b) (2 points) Calculate an estimate of (I using this maximum likelihood estimator when .761 = 043, 1'2 = 0.3, 353 = 12, ,I4 = 1.6. (b) (c) (2 points) Calculate an estimate of Va + 1 using this maximum likelihood estimator when :31 = 037 $2 = 0.3, $3 = 1.2, 7:54 = 1.6