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Introduction to Econometrics 3rd Edition by James Stock, James Stock
Edition 3ISBN: 978-9352863501Introduction to Econometrics 3rd Edition by James Stock, James Stock
Edition 3ISBN: 978-9352863501 Exercise 6
This exercise shows that the sample variance is an unbiased estimator of the population variance when Y₁... ,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 Y₁... ,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/SM2686/11eb9b5b_3d58_7b02_bf3e_0d289d154a06_SM2686_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 Y₁... ,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/SM2686/11eb9b5b_3d58_a213_bf3e_0da27704c657_SM2686_11.jpg)
) + var( ![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y₁... ,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/SM2686/11eb9b5b_3d58_a214_bf3e_adbca7dedf03_SM2686_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 Y₁... ,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/SM2686/11eb9b5b_3d58_a215_bf3e_d3e8f57b3766_SM2686_11.jpg)
,Y i ) = 2 Y /n.
c. Use the results in (a) and (b) to show that E(s 2 Y ) = 2 y.![This exercise shows that the sample variance is an unbiased estimator of the population variance when Y₁... ,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/SM2686/11eb9b5b_3d58_a216_bf3e_3522e5b6596c_SM2686_00.jpg)
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 me...
Introduction to Econometrics 3rd Edition by James Stock, James Stock
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