2.I.3H2 . \mathrm{I} . 3 \mathrm{H} \quad

Statistics | Part IB, 2002

Explain what is meant by a uniformly most powerful test, its power function and size.

Let Y1,,YnY_{1}, \ldots, Y_{n} be independent identically distributed random variables with common density ρeρy,y0\rho e^{-\rho y}, y \geq 0. Obtain the uniformly most powerful test of ρ=ρ0\rho=\rho_{0} against alternatives ρ<ρ0\rho<\rho_{0} and determine the power function of the test.

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