Exercise 17. Let X₁,..., Xn~ N(u, o2) be i.i.d. where u is known, but o2 is unknown. Considerthe estimaten1Σ(X₁-1for the variance.a) Show that7²C :=i=1-μ)²722·Σ( X ₁ = μ)² ~ x² (n).Oi=1b) For a € (0, 1), denote the a-quantile of x2 (n) by qn(a). Using this notation, find numbersan, bn E R such that P(o² bno²) = 2.5%.c) Using these results, develop a test which can be used to test the hypothesis Ho: o² = oagainst the alternative H₁: 02 08.d) Assume we have n = 100, μ = 0 and we have observed 2 = 4.81. Test the hypothesisHo: o² = 4 vs. H₁: o² #4 at significance level 5%.

Answered: Image /qna-images/answer/e57e4c73-a5cf-4054-81bc-908a747ab8cf.jpg

Answered: Exercise 17. Let X₁,..., Xn~ N(μ, o²)…

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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