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8. Let X, X be a random sample of size n = 2 from a population having gamma distribution with probability density function 1

8. Let X, X be a random sample of size n = 2 from a population having gamma distribution with probability density function 1 - x-1, f(x|a,0) = e x > 0, () where a > 0 and 0 > 0 are unknown parameters, and I'(a) is the usual gamma function. (a) Show that T = (X + X, XX) is a minimal sufficient statistic; (b) Are T = (ln(XX, X + X) and T = (In X + ln X, ln(X + X)) sufficient statistics; here, for any real number x, x| denotes the modulus of x; (c) Find the minimum variance unbiased estimator of V(X).

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