Suppose that we have two independent random samples: X1,..., Xn are exponential(θ), and Y1,..., Ym are exponential(μ).

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Suppose that we have two independent random samples: X1,..., Xn are exponential(θ), and Y1,..., Ym are exponential(μ).
(a) Find the LRT of H0: θ = μ versus H1: 0 ‰  μ.
(b) Show that the test in part (a) can be based on the statistic
ΣΧ. ΣΧ. + ΣY %3D

(c) Find the distribution of T when Ho is true.

Distribution
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Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

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