1. Background and Motivation

1.3 Summation Convention

For those of you who were ripped off in your high school education, a brief review of an important symbolic convention is given here. This convention will be used in the formulae that you will need to use.

The capital Greek Sigma, \sum, means sum or add. For example, suppose that you have 5 data sample values, represented abstractly by d_1, d_2, d_3, d_4 and d_5, or more abstractly (using set notation) by:

d_i, i\in\{1,2,3,4,5\} (or i=1,2,3,4,5)

If you want to add the 5 values you would write:

    \begin{align*}d_1 + d_2 + d_3 + d_4 + d_5\end{align*}



Sometimes people get lazy and leave off the limits on the summation sign \sum and write

    \begin{align*}\sum d_{i}\end{align*}

where it is hopefully clear that i is the summation index . We can also leave off the summation index and write

    \begin{align*}\sum d\end{align*}

just to remind us that we need to add up a bunch of numbers generically represented by d. This last convention is useful for us because whenever we need to deal with a sum in a formula, we will get that sum from adding up numbers in a table that we have constructed.