Let X have a Weibull distribution with parameters a and , so E(X) B T(1+1/) V(X) = B{T(1 + 2/a) - [T(1 + 1/a)]}

a. Based on a random sample X,..., X, write equations for the method of moments estimators of and

a. Show that, once the estimate of a has been obtained, the esti- mate of can be found from a table of the gamma func- tion and that the estimate of a is the solution to a complicated equation involving the gamma function.

b. If n = 20, x=28.0, and Ex? 16,500, compute the estimates. [Hint: [F(1.2)]/T(1.4) = .95.]