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Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X- Ν(μ2 -11,262). (b) Let X₁,..., X and Y₁,...,Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y₁ - X₁, construct a (1-a)-confidence interval [an, bn] for μ₂-μ₁. (c) Take [an, bn] from part (b). Recall that μ₂>₁>0. Show that P{0 € [an, bn]}-0 (n →∞o).

Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X- Ν(μ2 -11,262). (b) Let X₁,..., X and Y₁,...,Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y₁ - X₁, construct a (1-a)-confidence interval [an, bn] for μ₂-μ₁. (c) Take [an, bn] from part (b). Recall that μ₂>₁>0. Show that P{0 € [an, bn]}-0 (n →∞o).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X - Ν(μ2 - 11,207). (b) Let X₁,..., X and Y₁,..., Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y; - Xi, construct a (1-a)-confidence interval [an, bn] for μ2-μ1. (c) Take [an, bn] from part (b). Recall that ₂ >₁ > 0. Show that P{0 € [an, bn]} → 0 (n →∞o).
Transcribed Image Text:Problem 6 (a) Let X-N(μ1,02) and Y-N(μ2,02) be independent, where μ2> μ₁>0. Show that Y-X - Ν(μ2 - 11,207). (b) Let X₁,..., X and Y₁,..., Yn be i.i.d. copies of X and Y. Using the variables Z₁ = Y; - Xi, construct a (1-a)-confidence interval [an, bn] for μ2-μ1. (c) Take [an, bn] from part (b). Recall that ₂ >₁ > 0. Show that P{0 € [an, bn]} → 0 (n →∞o).
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