E1X 2 = b # f11 + 1/a 2
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V1X 2 = b25f11 + 2/a 2 – 3 f11 + 1/a 26
a. Based on a random sample X1, . . . , Xn, write equations for the method of moments estimators of b and a. Show that, once the estimate of a has been obtained, the estimate of b can be found from a table of the gamma function and that the estimate of a is the solution to a complicated equation involving the gamma function.
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b. If n = 20, x = 28.0, and g x 2 = 16,500, com- pute the estimates. (Hint: [f(1.2)]2/f(1.4) = .95.)