Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Textbook Question

Chapter 4.3, Problem 35E

If Y is a continuous random variable such that E[(Y − a)²] < ∞ for all a, show that E[(Y − a)²] is minimized when a = E(Y). [Hint: E[(Y − a)²] = E({[Y − E(Y)] + [E(Y) − a]}²).]

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Chapter 4.3, Problem 34E

Chapter 4.3, Problem 36E

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Mathematical Statistics with Applications

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If Y is a continuous random variable such that E [( Y − a ) 2 ] < ∞ for all a , show that E [( Y − a ) 2 ] is minimized when a = E ( Y ). [ Hint: E [( Y − a ) 2 ] = E ({[ Y − E ( Y )] + [ E ( Y ) − a ]} 2 ).]

Solution Summary: The author explains how to prove that E(Y-a-)2right] is minimized when a=E (y ). Let c be

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Chapter 4 Solutions

If Y is a continuous random variable such that E [( Y − a ) 2 ] &lt; ∞ for all a , show that E [( Y − a ) 2 ] is minimized when a = E ( Y ). [ Hint: E [( Y − a ) 2 ] = E ({[ Y − E ( Y )] + [ E ( Y ) − a ]} 2 ).]

Solution Summary: The author explains how to prove that E(Y-a-)2right] is minimized when a=E (y ). Let c be

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Chapter 4 Solutions

If Y is a continuous random variable such that E [( Y − a ) 2 ] < ∞ for all a , show that E [( Y − a ) 2 ] is minimized when a = E ( Y ). [ Hint: E [( Y − a ) 2 ] = E ({[ Y − E ( Y )] + [ E ( Y ) − a ]} 2 ).]