Let X1,..., X, be a random sample of distribution f(r;0) =e-(=/0)*, r>0, 0> 0. (a) Find the mle of 0. (b) Find the Likelihood ratio test for Ho: 0 = 00 vs Ha : 0 00 at the significance level a = 0.05. %3D

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Let X1,..., X, be a random sample of distribution f(x; 0)
= e-(z/0)*, x > 0, 0>0.
(a) Find the mle of 0.
(b) Find the Likelihood ratio test for Ho : 0 = 00 vs H. : 0 + 0o at the significance level
a = 0.05.
(c) Find the UMP test for testing Ho : 0 = 1 vs H. : 0 > 1 at the significance level
a = 0.05.
Transcribed Image Text:Let X1,..., X, be a random sample of distribution f(x; 0) = e-(z/0)*, x > 0, 0>0. (a) Find the mle of 0. (b) Find the Likelihood ratio test for Ho : 0 = 00 vs H. : 0 + 0o at the significance level a = 0.05. (c) Find the UMP test for testing Ho : 0 = 1 vs H. : 0 > 1 at the significance level a = 0.05.
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