Question: Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 01) = 01e01, 0 x < and 0 > 0 and

Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 0) = 0e-0, 0x 0 and Y1, Y2, Yn denote

Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 01) = 01e01, 0 x < and 0 > 0 and Y1, Y2, Yn denote an independent random sample from f(y; 02) = 02e-024 0yo and 02 > 0. The likelihood ratio test for Ho: 0 = 02 versus H: 01 02 is: m+n mx+ny (m+n) (x)" (y)" Show that the likelihood ratio test can be expressed in terms of the statistic T = + Show that the above statistic T follows a beta distribution under Ho: 0 = 0 = 0.

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