EXCERSICE 3. Let X1,..., Xn be iid observations from a location-scale family. Let T1(X1,...,Xn) and T2(X1,..., Xn) be two statistics that both satisfy T:(axı + b, ..., axn + b) = aT:(I1,..., In) for all values of x1,..., In and b and for any a > 0. (a) Show that T1/T2 is an ancillary statistic. (b) Let R be the sample range and S be the sample standard deviation. Verify that R and S satisfy the above condition so that R/S is an ancillary statistic. Dr. Asieh Abtahi - Faculty of Mathematics and Statistics - Islamic Azad University of Shiraz - Iran 13

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