4. Consider a random sample {Xi, i = 1, 2, ...n} of size n from a distribution with pdf f(x; 8) = 0(1+ x)-(1+0) if x > 0, and 0 otherwise. %3D (a) Show that the maximum likelihood estimator (mle) Ô of e is a function of E- In(1+ X;) (b) Let Y = In (1+X), find pdf of Y and mgf of Y. (c) Using result (b) to show that Z = E In(1 + X;) has a Gamma distribution. Specify the parameters of the gamma distribution (hint: find mgf of Z)

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