3 3.Let Y1, Y2,,Y, be i.i.d sample from a sub-family of Gamma distributions withdensity f(y|0) = ye-w/ /0°,y > 0.(i) Find the maximum likelihood cstimator of e.(ii) Find a method of moment estimator of 0.(iii) Find the asymptotic (large sample) distribution of the MLE obtained in part (i).(iv) Carry out a large sample Wald test for Ho : 0 = 1 v.s. H :0 +1 based on the result in (ii).

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Let Y1, Y2, --Y be ii.d sample from a sub-family of Gamma distributions with 3. density f(y|0) = ye-y//02,y > 0. (i) Find the maximum likelihood estimator of 0. (ii) Find a method of moment cstimator of 0. (ii) Find the asymptotic (large sample) distribution of the MLE obtained in part (i).