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
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
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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.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F707cac12-b30c-449e-8c7f-ec7366c048b1%2Ffc4a9190-4cb0-461b-940c-727414e1517c%2F2id5c6l_processed.jpeg&w=3840&q=75)
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.*
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