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Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
Edition 3ISBN: 978-9352863501Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
Edition 3ISBN: 978-9352863501 Exercise 10
This exercise shows that the sample variance is an unbiased estimator of the population variance when Y 1... ,Y n are i.i.d. with mean y variance 2 y.
a. Use Equation (2.31) to show that E[(Y i -
![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y 1... ,Y n are i.i.d. with mean y variance 2 y. a. Use Equation (2.31) to show that E[(Y i - ) 2 ] = var( Y i ) - 2 cov( Y i , ) + var( ). b. Use Equation (2.33) to show that cov( ,Y i ) = 2 Y /n. c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.](https://d2lvgg3v3hfg70.cloudfront.net/SM2685/11eb817c_773e_2008_84e6_cb45b4e209ae_SM2685_11.jpg)
) 2 ] = var( Y i ) - 2 cov( Y i ,
![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y 1... ,Y n are i.i.d. with mean y variance 2 y. a. Use Equation (2.31) to show that E[(Y i - ) 2 ] = var( Y i ) - 2 cov( Y i , ) + var( ). b. Use Equation (2.33) to show that cov( ,Y i ) = 2 Y /n. c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.](https://d2lvgg3v3hfg70.cloudfront.net/SM2685/11eb817c_773e_4719_84e6_232303c8fc9e_SM2685_11.jpg)
) + var(
![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y 1... ,Y n are i.i.d. with mean y variance 2 y. a. Use Equation (2.31) to show that E[(Y i - ) 2 ] = var( Y i ) - 2 cov( Y i , ) + var( ). b. Use Equation (2.33) to show that cov( ,Y i ) = 2 Y /n. c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.](https://d2lvgg3v3hfg70.cloudfront.net/SM2685/11eb817c_773e_471a_84e6_a5c08b77364c_SM2685_11.jpg)
).
b. Use Equation (2.33) to show that cov(
![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y 1... ,Y n are i.i.d. with mean y variance 2 y. a. Use Equation (2.31) to show that E[(Y i - ) 2 ] = var( Y i ) - 2 cov( Y i , ) + var( ). b. Use Equation (2.33) to show that cov( ,Y i ) = 2 Y /n. c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.](https://d2lvgg3v3hfg70.cloudfront.net/SM2685/11eb817c_773e_471b_84e6_a7920fc01dbe_SM2685_11.jpg)
,Y i ) = 2 Y /n.
c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.
a. Use Equation (2.31) to show that E[(Y i -
) 2 ] = var( Y i ) - 2 cov( Y i , ) + var( ).b. Use Equation (2.33) to show that cov(
,Y i ) = 2 Y /n. c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.
Explanation
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Given:
are IID random variables with ...
Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
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