Forensic Systems Engineering

Appendix CBrief Review of Probability and Statistics

CHAPTER MENU

1. C.1 Measures of Location
2. C.1.1 Average: The Mean Value
3. C.1.2 Average: The Median
4. C.1.3 Average: The Mode
5. C.2 Measures of Dispersion
6. C.2.1 Variance
7. C.2.2 Range
8. C.3 Distributions
9. C.3.1 Continuous Distributions
10. C.3.2 Discrete Distributions
11. C.4 Tests of Hypotheses
12. C.4.1 Estimating Parametric Change
13. C.4.2 Confidence Level
14. C.5 Ordered Statistics
15. References

Statistics has been defined as making sense out of data. The two major branches of statistics are probability and statistical inference. Probability is a methodology used to describe the random variation of data; in our case, systems data. The range of values in a set of data may vary and we may not know its average value exactly if the population we are examining is very large. For example, we cannot know the average number of salmon in the Columbia River in any given year. Nor can we know exactly the average value of a product made by a company as long as it continues making them, because all the while that production continues, the population is changing values.

The average value and standard deviation of a random variable are called parameters. Statisticians use a convention to distinguish the true values of the parameters, which we often do not know, and the measures taken of them. True values are labeled by Greek symbols. The true mean value of a set is often labeled by μ; the true standard deviation of the set is always labeled by σ. Measured values ...