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Write the bivariate normal pdf f (x, y; ?1, ?2, ?3, ?4,

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 3E Chapter 6.7

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 3E

Write the bivariate normal pdf \(f\left(x, y ; \theta_{1}, \theta_{2^{\prime}}, \theta_{3^{\prime}} \theta_{4}, \theta_{5}\right)\) in exponential form and show that \(Z_{1}=\sum_{i=1}^{n} X_{i}^{2}, Z_{2}=\sum_{i=1}^{n} Y_{i}^{2}, \quad Z_{3}=\sum_{i=1}^{n} X_{i} Y_{i^{\prime}} \quad Z_{4}=\sum_{i=1}^{n} X_{i}\), and \(Z_{5}=\sum_{i=1}^{n} Y_{i}\) are joint sufficient statistics for\(\theta_{1}, \theta_{2^{\prime}} \theta_{3} \theta_{4}\), and \(\theta_{5}\)

Equation Transcription:

, 

 ,

Text Transcription:

 f(x,y;theta_1,theta_2,theta_3,theta_4,theta_5

Z_1=sum_i=1^n X_i^2, Z_2=sum_i=1^n Y_i^2,   Z_3=sum_i=1^n X_i Y_i,    Z_4=sum_i=1^n X_i

Z_5=sum_i=1^n Y_i

theta_1,theta_2,theta_3,theta_4

theta_5

Step-by-Step Solution:

Step 1 of 6

To show:- , , ,  and  are joint sufficient statistics for , , ,  and .

Step 2 of 6

Chapter 6.7, Problem 3E is Solved
Step 3 of 6

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

Since the solution to 3E from 6.7 chapter was answered, more than 368 students have viewed the full step-by-step answer. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The full step-by-step solution to problem: 3E from chapter: 6.7 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “?Write the bivariate normal pdf \(f\left(x, y ; \theta_{1}, \theta_{2^{\prime}}, \theta_{3^{\prime}} \theta_{4}, \theta_{5}\right)\) in exponential form and show that \(Z_{1}=\sum_{i=1}^{n} X_{i}^{2}, Z_{2}=\sum_{i=1}^{n} Y_{i}^{2}, \quad Z_{3}=\sum_{i=1}^{n} X_{i} Y_{i^{\prime}} \quad Z_{4}=\sum_{i=1}^{n} X_{i}\), and \(Z_{5}=\sum_{i=1}^{n} Y_{i}\) are joint sufficient statistics for\(\theta_{1}, \theta_{2^{\prime}} \theta_{3} \theta_{4}\), and \(\theta_{5}\)Equation Transcription:, ,Text Transcription: f(x,y;theta_1,theta_2,theta_3,theta_4,theta_5Z_1=sum_i=1^n X_i^2, Z_2=sum_i=1^n Y_i^2, Z_3=sum_i=1^n X_i Y_i, Z_4=sum_i=1^n X_iZ_5=sum_i=1^n Y_itheta_1,theta_2,theta_3,theta_4theta_5” is broken down into a number of easy to follow steps, and 56 words. This full solution covers the following key subjects: bivariate, Exponential, form, normal, pdf. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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Write the bivariate normal pdf f (x, y; ?1, ?2, ?3, ?4,