Let Y1 and Y2 be independent and identically distributed

Chapter 10, Problem 5E

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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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