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2. Find the method of moments estimators for a and b for the continuous uniform distribution. (see page 136).

2. Find the method of moments estimators for a and b for the continuous uniform distribution. (see page 136).

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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## Statistical Analysis Activity ### Background 1. In an introductory statistics class, students were paired to conduct a survey and perform statistical analyses. Alex and Morgan partnered up to ask, "How many minutes do you exercise in a week?" Alex surveyed 10 peers and calculated a sample mean, while Morgan asked 20 different peers and also calculated a sample mean. ### Task To compute a combined mean, Alex and Morgan considered two options: - **Alex's Proposal**: Average the two sample means using the formula: \[ \hat{\mu} = \frac{\bar{x}_{\text{Alex}} + \bar{x}_{\text{Morgan}}}{2} \] - **Morgan's Proposal**: Combine all 30 responses into one dataset and calculate the overall mean. ### Questions a) Demonstrate that both Alex's and Morgan's estimators are unbiased. b) Identify which estimator has a smaller variance. Show your calculations and reasoning. ### Additional Problem 2. Use the method of moments to estimate parameters \(a\) and \(b\) for the continuous uniform distribution. Refer to page 136 for further guidance.
Transcribed Image Text:## Statistical Analysis Activity ### Background 1. In an introductory statistics class, students were paired to conduct a survey and perform statistical analyses. Alex and Morgan partnered up to ask, "How many minutes do you exercise in a week?" Alex surveyed 10 peers and calculated a sample mean, while Morgan asked 20 different peers and also calculated a sample mean. ### Task To compute a combined mean, Alex and Morgan considered two options: - **Alex's Proposal**: Average the two sample means using the formula: \[ \hat{\mu} = \frac{\bar{x}_{\text{Alex}} + \bar{x}_{\text{Morgan}}}{2} \] - **Morgan's Proposal**: Combine all 30 responses into one dataset and calculate the overall mean. ### Questions a) Demonstrate that both Alex's and Morgan's estimators are unbiased. b) Identify which estimator has a smaller variance. Show your calculations and reasoning. ### Additional Problem 2. Use the method of moments to estimate parameters \(a\) and \(b\) for the continuous uniform distribution. Refer to page 136 for further guidance.
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