Let X have a Weibull distribution with parameters a and b, so E(X) = (1 + 1/) V(X) = 2(1 + 2/) -

Let X have a Weibull distribution with parameters a and b, so
E(X) = β ∙ Γ(1 + 1/α)
V(X) = β2Γ(1 + 2/α) - [Γ(1 + 1/α)]2}
a. Based on a random sample X1,..., Xn, write equations for the method of moments estimators of β and α. Show that, once the estimate of α has been obtained, the estimate of β can be found from a table of the gamma function and that the estimate of α is the solution to a complicated equation involving the gamma function.
b. If n = 20, x = 28.0, and ΣXi2 = 16,500, compute the estimates.