Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 01) = 01e01,...

 

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Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 01) = 01e01, 0≤ x < ∞ and 0₁ > 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: 0₁ = 02 versus H₁: 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 = ΣΧ ΣΧ+ΣΥ Show that the above statistic T follows a beta distribution under Ho: 0₁ = 0₂ = 0. Let X1, X2, ..., Xm denote an independent random sample from -01x f(x; 01) = 01e01, 0≤ x < ∞ and 0₁ > 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: 0₁ = 02 versus H₁: 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 = ΣΧ ΣΧ+ΣΥ Show that the above statistic T follows a beta distribution under Ho: 0₁ = 0₂ = 0.