Consider drawing samples of sizen = 12 from U(0,12) Consider estimators for the population variance. One such estimator is the familiar s'. When you draw such a sample, what is E(s') ? Another is the sample range r, where r = ymax - Ymin When you draw such a sample, what is E(r) ? Hint: E(y max) = 144/13 using Theorem 3.10.1

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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**Variance Estimation from Uniform Distribution**

Consider drawing samples of size \( n = 12 \) from a uniform distribution \( U(0,12) \).

### Estimators for the Population Variance

- **Estimator \( s^2 \):**  
  When you draw such a sample, what is \( E(s^2) \)?
  - *[Blank for student input]*

- **Sample Range \( r \):**  
  Another estimator is the sample range \( r \), where \( r = y_{\text{max}} - y_{\text{min}} \).
  When you draw such a sample, what is \( E(r) \)?
  - Hint: \( E(y_{\text{max}}) = \frac{144}{13} \) using Theorem 3.10.1.
  - *[Blank for student input]*

**Questions:**

- Is \( r \) unbiased?
  - *[Blank for student input]*
  
- Is \( r \) consistent?
  - *[Blank for student input]*

*Note: The highlighted areas are intended for answers or notes by the educator or student.*
Transcribed Image Text:**Variance Estimation from Uniform Distribution** Consider drawing samples of size \( n = 12 \) from a uniform distribution \( U(0,12) \). ### Estimators for the Population Variance - **Estimator \( s^2 \):** When you draw such a sample, what is \( E(s^2) \)? - *[Blank for student input]* - **Sample Range \( r \):** Another estimator is the sample range \( r \), where \( r = y_{\text{max}} - y_{\text{min}} \). When you draw such a sample, what is \( E(r) \)? - Hint: \( E(y_{\text{max}}) = \frac{144}{13} \) using Theorem 3.10.1. - *[Blank for student input]* **Questions:** - Is \( r \) unbiased? - *[Blank for student input]* - Is \( r \) consistent? - *[Blank for student input]* *Note: The highlighted areas are intended for answers or notes by the educator or student.*
Expert Solution
Step 1

n = 12

X ~ U(0,12)

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