Appendix_VI_distributions

Appendix_VI_distributions - Appendix VI Probability...

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1 Appendix VI. Probability Distributions Appendix VI. Probability Distributions Revised July 2, 2004 A. Introduction You will encounter several probability distributions in the course of your experi- ments in physics. The most common are the Gaussian distribution (also known as the Bell curve or normal distribution), the Poisson distribution and the exponential distribution . While modern computer pro- grams may greatly simplify the handling of these distributions, science and engineering students should have an understanding of their basic properties and of the problems to which each may apply. In this Appendix we present the normalized form of each distri- bution, e.g., the expression that gives unity when summed or integrated over the allowed range of the distribution. B. Gaussian Distribution The Gaussian distribution is the most common probability distribution in science. Repeated, independent measurements with random uncertainties of almost any quantity follow this distribution. For example, the numbers of heads and tails you are likely to find if you flip a coin many times is described by a Gaussian distribution. When a large physics class is given an exam, a Gaussian distribution may describe the grades for the class. The Gaussian is characterized by two parameters; the mean, , and the standard deviation, . The normalized Gaussian is expressed as   dx e dx x P x 2 2 2 2 1 (1) The term ‘normalized’ refers to a scaling of the distribution function so that the area under the curve equals unity.

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