HW #2 solution - STAT 420 Homework #2 (10 points) (due...

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STAT 420 Spring 2007 Homework #2 (10 points) (due Friday, February 2, by 4:00 p.m.) From the textbook: 4.5 Prove the algebraic identity ( ) ( ) ( ) & & & & & = = = = = - + - = - J j n i j ij J j j J j n i ij Y Y Y Y n Y Y 1 1 2 1 2 1 1 2 ( ) ( ) & & & & = = = = - + - = - J j n i j j ij J j n i ij j j Y Y Y Y Y Y 1 1 2 1 1 2 = ( ) ( ) ( ) ( ) & & & & & & = = = = = = - + - - + - J j n i j J j n i j j ij J j n i j ij j j j Y Y Y Y Y Y Y Y 1 1 2 1 1 1 1 2 2 = ( ) ( ) ( ) ( ) & & & & & = = = = = - + - - + - J j j j J j n i j ij j J j n i j ij Y Y n Y Y Y Y Y Y j j 1 2 1 1 1 1 2 2 . Since ( ) & = - j n i j ij Y Y 1 = 0, j = 1, … , J , ( ) ( ) & & = = - - J j n i j ij j j Y Y Y Y 1 1 2 = 0, and ( ) ( ) ( ) & & & & & = = = = = - + - = - J j j j J j n i j ij J j n i ij Y Y n Y Y Y Y j j 1 2 1 1 2 1 1 2 . OR ( ) 2 1 1 1 1 2 1 1 2 2 1 1 2 2 2 Y Jn Y Y Y Y Y Y Y Y Y J j n i ij J j n i ij J j n i ij ij J j n i ij + - = ± ² ³ ´ µ + - = - & & & & & & & & = = = = = = = = = ( ) 2 1 1 2 2 1 1 2 2 Y Jn Y Y Jn Y Jn Y Y J j n i ij J j n i ij - = + - & & & & = = = = .
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( ) 2 1 1 2 1 2 2 1 2 2 2 Y Jn Y n Y Y n Y Y Y Y n Y Y n J j j J j j J j j j J j j + - = & ± ² ³ ´ µ + - = - = = = = = ( )
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4.6 The American Car Company is interested in the average number of cars coming off three assembly lines with obvious defects (determined by visual inspection). The number of defects per week for each of the assembly lines is recorded for several weeks. The data follow.
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This note was uploaded on 12/17/2010 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.

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HW #2 solution - STAT 420 Homework #2 (10 points) (due...

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