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6) 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)=()1x
1exI(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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