6.4.2. Let X₁, X2,..., Xn and Y₁, Y2,..., Ym be independent random samples from N (01,03) and N(02, 04) distributions, respectively. (a) If C R³ is defined by Ω = = {(01,02,03): -∞ < 0₁ <∞, i = 1,2; 0 < 03 = 04 <∞0}, find the mles of 01, 02, and 03. (b) If NC R2 is defined by = {(01,03): -∞ < 0₁ = 0₂ <∞x; 0 < 03 = 04 <∞0},
6.4.2. Let X₁, X2,..., Xn and Y₁, Y2,..., Ym be independent random samples from N (01,03) and N(02, 04) distributions, respectively. (a) If C R³ is defined by Ω = = {(01,02,03): -∞ < 0₁ <∞, i = 1,2; 0 < 03 = 04 <∞0}, find the mles of 01, 02, and 03. (b) If NC R2 is defined by = {(01,03): -∞ < 0₁ = 0₂ <∞x; 0 < 03 = 04 <∞0},
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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![**6.4.2.** Let \( X_1, X_2, \ldots, X_n \) and \( Y_1, Y_2, \ldots, Y_m \) be independent random samples from \( N(\theta_1, \theta_3) \) and \( N(\theta_2, \theta_4) \) distributions, respectively.
(a) If \( \Omega \subset R^3 \) is defined by
\[
\Omega = \{ (\theta_1, \theta_2, \theta_3) : -\infty < \theta_i < \infty, \, i = 1, 2; \, 0 < \theta_3 = \theta_4 < \infty \},
\]
find the MLEs of \( \theta_1, \theta_2, \) and \( \theta_3 \).
(b) If \( \Omega \subset R^2 \) is defined by
\[
\Omega = \{ (\theta_1, \theta_3) : -\infty < \theta_1 = \theta_2 < \infty; \, 0 < \theta_3 = \theta_4 < \infty \},
\]
find the MLEs of \( \theta_1 \) and \( \theta_3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F718b1378-40e4-4c32-83bc-211fc46d7de4%2F4a4b1705-fdd9-4ba3-a2aa-a6960bcc06f3%2Fm9niem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**6.4.2.** Let \( X_1, X_2, \ldots, X_n \) and \( Y_1, Y_2, \ldots, Y_m \) be independent random samples from \( N(\theta_1, \theta_3) \) and \( N(\theta_2, \theta_4) \) distributions, respectively.
(a) If \( \Omega \subset R^3 \) is defined by
\[
\Omega = \{ (\theta_1, \theta_2, \theta_3) : -\infty < \theta_i < \infty, \, i = 1, 2; \, 0 < \theta_3 = \theta_4 < \infty \},
\]
find the MLEs of \( \theta_1, \theta_2, \) and \( \theta_3 \).
(b) If \( \Omega \subset R^2 \) is defined by
\[
\Omega = \{ (\theta_1, \theta_3) : -\infty < \theta_1 = \theta_2 < \infty; \, 0 < \theta_3 = \theta_4 < \infty \},
\]
find the MLEs of \( \theta_1 \) and \( \theta_3 \).
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