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Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0

Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0

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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**Question 10:** Let \( x_1, x_2, \ldots, x_n \) be a random sample from a continuous uniform distribution with domain (0, b). This means that \( f(x) = 1/b \) for \( 0 < x < b \). Is \( 2 \times \bar{x} \) an unbiased estimator for \( b \)? *For the instructor, this was question 4.* - [✔] Yes, because \( E(X) = (1/2) \times b \), so \( E(\bar{X}) = (1/2) \times b \), so \( E(2 \times \bar{X}) = b \). - [✘] Yes, because \( 2 \times \bar{x} \) is the method of moments estimator for \( b \). - [✘] No, because the sample mean would be an unbiased estimator, not 2 times that value. - [✘] No, because \( 2 \times \bar{x} \) could give you a value smaller than the largest data point. - [✘] It depends on the sample size (how large \( n \) is).
Transcribed Image Text:**Question 10:** Let \( x_1, x_2, \ldots, x_n \) be a random sample from a continuous uniform distribution with domain (0, b). This means that \( f(x) = 1/b \) for \( 0 < x < b \). Is \( 2 \times \bar{x} \) an unbiased estimator for \( b \)? *For the instructor, this was question 4.* - [✔] Yes, because \( E(X) = (1/2) \times b \), so \( E(\bar{X}) = (1/2) \times b \), so \( E(2 \times \bar{X}) = b \). - [✘] Yes, because \( 2 \times \bar{x} \) is the method of moments estimator for \( b \). - [✘] No, because the sample mean would be an unbiased estimator, not 2 times that value. - [✘] No, because \( 2 \times \bar{x} \) could give you a value smaller than the largest data point. - [✘] It depends on the sample size (how large \( n \) is).
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