Appendix IV: Some Performance Math

General Math

Sums and Products

*Summation:* The symbol Σ (Greek upper case *sigma*) denotes a summation of items. The example below should make the function clear.

$${\mathrm{a}}_{1}+{\mathrm{a}}_{2}+{\mathrm{a}}_{3}+\dots {\mathrm{a}}_{\mathrm{n}}=\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}}$$

*Product:* The symbol Π (Greek upper case *pi*) denotes a product of items. The example below should make the function clear.

$${\mathrm{a}}_{1}\times {\mathrm{a}}_{2}\times {\mathrm{a}}_{3}\times \dots {\mathrm{a}}_{\mathrm{n}}=\prod _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}}$$

Mean Values of Quantities

The use of means or averages of some sort are common in IT since very few measurable parameters always have a fixed value. There are *mean response times, mean reliabilities, average utilizations*, and so on, often depending on mathematical distributions for their derivation and calculation.

Arithmetic Mean (Average)

This is the most common type of average. If we have ...

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