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c. Let X1, X2, ..., Xn be independent and X; ~ N(iµ,o²), where u and o? are unknown parameters. Find the maximum likelihood estimate of µ.

c. Let X1, X2, ..., Xn be independent and X; ~ N(iµ,o²), where u and o? are unknown parameters. Find the maximum likelihood estimate of µ.

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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Part C

a. Suppose X ~I(3,B). If a random sample of size n is selected from this distribution, find the form of the critical region of the most powerful test using the Neyman-Pearson lemma for testing: %3| На : В — Ва, with Ba > Bo- :4, Bo = 4, and a = 0.05. Find and exact numerical value of the b. Refer to question (a). Suppose n = rejection region. Here a = 3 as in question (a) above. c. Let X1, X2, ..., Xn be independent and X; N(iu, o2), where u and o² are unknown parameters. Find the maximum likelihood estimate of d. Refer to question (a). Find the information matrix I(µ, o²). You may want to use E i2 n(n+1)(2n+1) in your answer. 6
Transcribed Image Text:a. Suppose X ~I(3,B). If a random sample of size n is selected from this distribution, find the form of the critical region of the most powerful test using the Neyman-Pearson lemma for testing: %3| На : В — Ва, with Ba > Bo- :4, Bo = 4, and a = 0.05. Find and exact numerical value of the b. Refer to question (a). Suppose n = rejection region. Here a = 3 as in question (a) above. c. Let X1, X2, ..., Xn be independent and X; N(iu, o2), where u and o² are unknown parameters. Find the maximum likelihood estimate of d. Refer to question (a). Find the information matrix I(µ, o²). You may want to use E i2 n(n+1)(2n+1) in your answer. 6
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