21. Let X have a Weibull distribution with parameters  and

, so E(X)

(1 1/)

V(X)
2

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

}

a. Based on a random sample X1, . . . , Xn, write equations for the method of moments estimators of  and . Show that, once the estimate of  has been obtained, the estimate of  can be found from a table of the gamma function and that the estimate of  is the solution to a complicated equation involving the gamma function.

b. If n
20, x
28.0, and
x2 i
16,500, compute the estimates. [Hint: [(1.2)]2

/(1.4)
.95.]