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9.57 Refer to Exercise 9.18. Is the estimator of o² given there an MVUE of o²?

9.57 Refer to Exercise 9.18. Is the estimator of o² given there an MVUE of 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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Answer 9.57

**9.57** Refer to Exercise 9.18. Is the estimator of \(\sigma^2\) given there an MVUE of \(\sigma^2\)?
Transcribed Image Text:**9.57** Refer to Exercise 9.18. Is the estimator of \(\sigma^2\) given there an MVUE of \(\sigma^2\)?
**9.17** Suppose that \( X_1, X_2, \ldots, X_n \) and \( Y_1, Y_2, \ldots, Y_n \) are independent random samples from populations with means \( \mu_1 \) and \( \mu_2 \) and variances \( \sigma_1^2 \) and \( \sigma_2^2 \), respectively. Show that \( \overline{X} - \overline{Y} \) is a consistent estimator of \( \mu_1 - \mu_2 \). **9.18** In Exercise 9.17, suppose that the populations are normally distributed with \( \sigma_1^2 = \sigma_2^2 = \sigma^2 \). Show that \[ \frac{\sum_{i=1}^{n} (X_i - \overline{X})^2 + \sum_{i=1}^{n} (Y_i - \overline{Y})^2}{2n - 2} \]
Transcribed Image Text:**9.17** Suppose that \( X_1, X_2, \ldots, X_n \) and \( Y_1, Y_2, \ldots, Y_n \) are independent random samples from populations with means \( \mu_1 \) and \( \mu_2 \) and variances \( \sigma_1^2 \) and \( \sigma_2^2 \), respectively. Show that \( \overline{X} - \overline{Y} \) is a consistent estimator of \( \mu_1 - \mu_2 \). **9.18** In Exercise 9.17, suppose that the populations are normally distributed with \( \sigma_1^2 = \sigma_2^2 = \sigma^2 \). Show that \[ \frac{\sum_{i=1}^{n} (X_i - \overline{X})^2 + \sum_{i=1}^{n} (Y_i - \overline{Y})^2}{2n - 2} \]
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