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Consider a random sample X1,,Xn of size n from a Gamma(,) population, where >0 is the shape parameter and >0 is the scale parameter. The density of function of X1 is given by f(x)=()1x1exI(x >0) Suppose that is known. (a) Find the maximum likelihood estimator of ; (b) It is known that the population variance is 2. Find the MLE of the population variance. Hint: use the invariance property of MLE..

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Consider a random sample X1,,Xn of size n from a Gamma(,) population, where >0 is the shape parameter and >0 is the scale parameter. The density of function of X1 is given by f(x)=()1x1exI(x >0) Suppose that is known. (a) Find the maximum likelihood estimator of ; (b) It is known that the population variance is 2. Find the MLE of the population variance. Hint: use the invariance property of MLE.

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