2002-54.md

course	course_year	question_number	tags	title	year
Statistics	IB	54	IB 2002 Statistics	$2 . \mathrm{I} . 3 \mathrm{H} \quad$	2002

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

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