We have talked about the fact that the sample mean estimator X = X; is an unbiased estimator of the mean u for identically distributed X1, X2, ..., Xn: E[X] = variance estimator, on the other hand, is not an unbiased estimate of the true variance o²: for µ. The straightforward Vý = E1(X; – X)², we get that E[V½] = (1 – )o². Instead, the following bias-corrected sample variance estimator is unbiased: V = „4 E (X; – X)². This unbiased estimator is typically what is called the sample variance. Use the fact that E[V] = o² to show that E[V] = (1 – )0². Hint: The proof is short, it can be done in a few lines. (b) that Var[X] = 02, for iid variables with variance o?. We can similarly ask what the variance is We also discussed the variance of the sample mean estimator, and concluded
We have talked about the fact that the sample mean estimator X = X; is an unbiased estimator of the mean u for identically distributed X1, X2, ..., Xn: E[X] = variance estimator, on the other hand, is not an unbiased estimate of the true variance o²: for µ. The straightforward Vý = E1(X; – X)², we get that E[V½] = (1 – )o². Instead, the following bias-corrected sample variance estimator is unbiased: V = „4 E (X; – X)². This unbiased estimator is typically what is called the sample variance. Use the fact that E[V] = o² to show that E[V] = (1 – )0². Hint: The proof is short, it can be done in a few lines. (b) that Var[X] = 02, for iid variables with variance o?. We can similarly ask what the variance is We also discussed the variance of the sample mean estimator, and concluded
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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