simple sigma operation question

• Sep 23rd 2012, 01:11 PM
kingsolomonsgrave
simple sigma operation question
How does one complete a summing operation where

$\displaystyle a = 11$ and $\displaystyle b= 96$

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

a sum like

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

where i is the index

i expanded it like this:

$\displaystyle (Y1-a-b)*X1 + (Y2-a-b)*X2 .... (Yn-a-b)*Xn$ 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!
• Sep 28th 2012, 06:07 PM
johnsomeone
Re: simple sigma operation question
You seem to understand it correctly.

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

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

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

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

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