Let Y 1 and Y 2 be a random sample of n = 2 observations from a

Question:

Let Y₁ and Y₂ be a random sample of n = 2 observations from a normal distribution with mean μ and variance σ².

a. Show that

has a standard normal distribution.

b. Given the result in part a, show that Z² possesses a χ2 distribution with 1 degree of freedom. First show that S² = (Y₁ - Y₂)²/2; then apply Theorem 6.11.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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Question Posted: May 17, 2021 07:54 AM

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Let Y 1 and Y 2 be a random sample of n = 2 observations from a

Question:

Y, - Y2 Z = V20

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ANSWER a To show that Z Y1 Y2sqrt2sigma has a standard normal distribution we need to calculate its ...View the full answer

Statistics For Engineering And The Sciences

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