Question: 121 7. Suppose X1. ..., X, is a random sample from the distribution with p.d.f f(x; a, B) = Set for a > a and

121 7. Suppose X1. ..., X, is a random sample from the distribution with p.d.f f(x; a, B) = Set for a > a and 0 elsewhere. Here both a and S are unknown positive parameters. Let X(1) = minskEn Xx. Here you can use the following fact with proof: the probability density function of T = log Xk d L x k=1 X(1) is f(t) = moth-le-at for t > 0. (a) Find the maximum likelihood estimator (MLE) of a and S, denoted by & and 3, respectively. [6 marks] (b) Find the limiting distribution of a. [4 marks] (c) Find appropriate constants a and o such that Vn(B - a) , N(0.62). In ( B - B)=NO , J(B ) ) ? [6 marks]

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