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3. Let Xiand zbe iid observations from the pdf f(r 0) = 010 e" € (0, 0); 0 € (0, x). Let Yi = log(X;) and Yz = log(-X2). Show that Yi/Yzis an anci...

Question

3. Let Xiand zbe iid observations from the pdf f(r 0) = 010 e" € (0, 0); 0 € (0, x). Let Yi = log(X;) and Yz = log(-X2). Show that Yi/Yzis an ancillary statistic. 1) Apply the technique of ranclom variable transformation and distribution marginalization. Apply the property of location-scale lamily.

3. Let Xiand zbe iid observations from the pdf f(r 0) = 010 e" € (0, 0); 0 € (0, x). Let Yi = log(X;) and Yz = log(-X2). Show that Yi/Yzis an ancillary statistic. 1) Apply the technique of ranclom variable transformation and distribution marginalization. Apply the property of location-scale lamily.



Answers

Let $X$ have a Weibull distribution. Verify that $\mu=\beta \Gamma(1+1 / \alpha) .[$Hint$:$ In the integral for $E(X)$ ) make the change of variable $y=(x / \beta)^{\alpha},$ so that $x=\beta y^{1 / \alpha} . ]$


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