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Math Help - simple sigma operation question

  1. #1
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    simple sigma operation question

    How does one complete a summing operation where

    a = 11 and b= 96

     X= {8, 10, 9} and        Y= {108, 101,103,94}

    a sum like

    i=1 and  n=4 for  sigma(Yi-a-b)Xi

    where i is the index


    i expanded it like this:

    (Y1-a-b)*X1 + (Y2-a-b)*X2 ....  (Yn-a-b)*Xn and in this case n = 4

    My question, assuming I expanded correctly, stands thus: since the set of X has only 3 elements so how do I compele this operation?

    thanks!
    Last edited by kingsolomonsgrave; September 23rd 2012 at 01:17 PM.
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  2. #2
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    Re: simple sigma operation question

    You seem to understand it correctly.

    \sum_{i=1}^{3} (Y_i - a - b)X_i = (Y_1 - a - b)X_1 + (Y_2 - a - b)X_2 + (Y_3 - a - b)X_3

    = ((108) - (11) - (96))(8) + ((101) - (11) - (96))(10) + ((103) - (11) - (96))(9)

    = (108 - 107)(8) + (101 - 107)(10) + (103 - 107)(9)

    = (1)(8) + (-6)(10) + (-4)(9) = 8 -60 - 36 = -88

    \sum_{i=1}^{4} (Y_i - a - b)X_i makes no sense, because there is no X_4 value given. It's undefined here.
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