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5. Suppose that X1, X2,..., Xn represent a random sample from N(0,0²). (a) Find the critical region of the most powerful test with significance level a to test Ho: 0² = σ versus Ha : 0² = σ²(> σ). (b) Find the ML estimator of σ². (c) Give a MVUE for σ². (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1 a CI for o².

5. Suppose that X1, X2,..., Xn represent a random sample from N(0,0²). (a) Find the critical region of the most powerful test with significance level a to test Ho: 0² = σ versus Ha : 0² = σ²(> σ). (b) Find the ML estimator of σ². (c) Give a MVUE for σ². (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1 a CI for o².

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. Suppose that X1, X2,..., Xn represent a random sample from N(0,0²). (a) Find the critical region of the most powerful test with significance level a to test Ho: 0² = σ versus Ha : 0² = σ²(> σ). (b) Find the ML estimator of σ². (c) Give a MVUE for σ². (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1 a CI for o².
Transcribed Image Text:5. Suppose that X1, X2,..., Xn represent a random sample from N(0,0²). (a) Find the critical region of the most powerful test with significance level a to test Ho: 0² = σ versus Ha : 0² = σ²(> σ). (b) Find the ML estimator of σ². (c) Give a MVUE for σ². (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1 a CI for o².
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