3. The Lévy distribution with parameter > 0 is characterized by having the density f(x; 0): {√ = (b) (a) Suppose we have samples x₁,..., n from the Lévy distribution with parameter 0. Find the maximum likelihood esti- mator for 0. (d) 270x3 exp(-20), Is your estimator from part (a) unbiased? 1 Hint: are samples from a Gamma distribution with parameters k = 1/2 and X = 1/(20). X1 Xn (c) x > 0 x ≤ 0 useful here as well. What is Var(). The hint from part (b) will be Show that the distribution of the samples 1/x1,..., 1/xn is in fact a Gamma distribution with the parameters spec- ified in the hint of part (b). It might be useful to know that I(1/2) = √T.

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