Let X have a Weibull distribution with parameters a and

b, so E(X) b (1  1/a)

V(X) b2

{(1  2/a) [(1  1/a)]2

}

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.

b. If n 20, 28.0, and , compute the estimates. [Hint: [(1.2)]2

/(1.4) .95.]