MIT2_854F10_ind_ex

MIT2_854F10_ind_ex - = 1 f " And (1) + g (2) + + g (6)...

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Notes for Lecture 3 Chuan Shi Example of Independence A = { i = 2 or 3 } ; B = { j = 1 or 5 or 6 } . Thus, we have AB {(2,1), (3,1),(2,5), (3,5), (2, 6), (3, 6)} . ∩= So, we can compute the following: ( ) = 12/36 ; PA = 1/3 PB () = 1 8 / 3 6 = 1 / 2 ; PA = ( ) ( ) ( B ) = 6 / 3 6 = 1 / 6 PAPB . We can also demonstrate the independence in the following way. Let
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() = f ( 2 )( 1 ) + f g + + f ( 2 )( 6 ) prob A g ( 2 )( 2 ) " g + f (3) (1) + f (3) (2) + + f g g g " (3) (6) = ( (2) + f (3))( (1) + g (2) + + g (6)) f g " Similarly, we have ( ) = ( (1) + g (5) + g (6))( (1) + f (2) + + f (6)) prob B g f " And ( B ) f g + f ( 3 )( 1 ) + f g + f ( 3 )( 5 ) + f g + f (
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Unformatted text preview: = 1 f " And (1) + g (2) + + g (6) = 1 g " Therefore, prob A ( ) = f (2) + f (3) ( ) = g (1) + g (5) + g (6) prob B Thus, ( ) ( ) = f + f (3))( (1) + g (5) + g (6)) prob A prob B ( (2) g (2) (1) + f (3) (1) + f g + f (3) (5) + f g + f (3) (6) = f g g (2) (5) g (2) (6) g ( B ) = prob A So, A and B are independent. MIT OpenCourseWare http://ocw.mit.edu 2.854 / 2.853 Introduction to Manufacturing Systems Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.854 taught by Professor Stanleygershwin during the Fall '10 term at MIT.

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MIT2_854F10_ind_ex - = 1 f " And (1) + g (2) + + g (6)...

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