31 An estimator is said to be consistent if for any 0, P( ) 0 0 as n 0 That is, is consistent if, as the sample size gets larger, it is less and less likely that will be further than from the true value of Show that X is a consistent estimator of when 2 by using Chebyshevs inequality from Exercise ...

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31. An estimator is said to be consistent if for any ! 0, P( ...

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31. An estimator ˆ

is said to be consistent if for any ! 0, P(⏐ˆ

⏐ !) 0 0 as n 0 . That is, ˆ

is consistent if, as the sample size gets larger, it is less and less likely that ˆ

will be further than ! from the true value of . Show that X is a consistent estimator of when 2 by using Chebyshev’s inequality from Exercise 44 of Chapter 3. [Hint:

The inequality can be rewritten in the form P(⏐Y Y⏐ !) 2 Y /!

Now identify Y with X.]

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Probability And Statistics For Engineering And The Sciences

ISBN: 9781111802325

7th Edition

Authors: Dave Ellis, Jay L Devore

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Question Posted: Sep 16, 2024 11:00 AM

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31. An estimator is said to be consistent if for any ! 0, P( ...

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Probability And Statistics For Engineering And The Sciences

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