Summation NotationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Summation NotationSummation NotationShorthand way of expressing a sumUses the Greek letter sigma: ∑nnkkaaaaa 3211k is called the index of summation n is called the upper limit of the summation ak is the formula used to generate each term of the sumSummation NotationAny letter can be used to index a summation nkknjjniiaaa111Summation NotationEx: Evaluate the following sum: Sol: 4132ii 32119753423323223123241iiSummation NotationEx: Evaluate the following sum:Sol: 6332jj 4815131193623523423323263jjSummation NotationRecall from Basic Probability, that for any two events E and F:If E and F are mutually exclusive, then P(E ∩ F) = 0, which means: FEPFPEPFEP FPEPFEP Summation NotationThe last statement can be generalized for several eventsFor events no two of which can take place at the same time, thennEEE ,,,21 niinnEPEPEPEPEEEP12121Summation notation is so much easier to writeSummation NotationProperties(i)(ii)Note: Not true nkknkknkkkbaba111nkknkkacac11 nkknkknkkkbaba111Summation NotationProperties (cont)(iii) for(iv) nmkkmkknkkaaa111nm 1 cncjcjniiaa11Summation NotationEx: Evaluate the following sum using (i) direct computation and (ii) Excel Sol: Direct computation 6112.12.1kkk 985984.1497664.041472.03456.0288.024.02.02.12.12.12.12.12.12.12.12.12.12.12.12.12.116615514413312211611kkkSummation NotationUsing Excelk1 0.22 0.243 0.2884 0.34565 0.414726 0.497664sum 1.985984 12.12.1kkSummation NotationUse Excel to evaluate . Round answers to 12 decimal places. Soln. 0.999999999713
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