Let Y1 and Y2 be independent and identically distributed
Chapter 10, Problem 5E(choose chapter or problem)
Let \(Y_{1} \text { and } Y_{2}\) be independent and identically distributed with a uniform distribution over the interval \((\theta, \theta+1)\). For testing \(H_{0}: \theta=0\) versus H_{a}: \theta>0\) we have two competing tests:
Test 1: Reject \(H_{0}\) if \(Y_{1}>.95\).
Test 2: Reject \(H_{0}\) if \(Y_{1}+Y_{2}>c\)
Find the value of so that test 2 has the same value for as test 1. [Hint: In Example 6.3, we derived the density and distribution function of the sum of two independent random variables that are uniformly distributed on the interval
Equation Transcription:
Text Transcription:
Y_1 and Y_2
(\theta, \theta+1)
H_0: \theta = 0
H_a: \theta > 0
Y_1 >.95
H_0
Y_1+Y_2 > c
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