# Probability Theory

Chapter

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## Abstract

The main goal of an experimental physicist is to measure quantities of interest, possibly with the best *precision*. In the luckiest cases, measurements lead to the *discovery* of new physical phenomena that may represent a breakthrough in the knowledge of Nature. Measurements, and, more in general, observations of Nature’s behavior, are performed with experiments that record quantitative information about the physical phenomenon under observation.

### References

- 1.Laplace, P.: Essai Philosophique Sur les Probabilités, 3rd edn. Courcier Imprimeur, Paris (1816)Google Scholar
- 2.Kolmogorov, A.: Foundations of the Theory of Probability. Chelsea, New York (1956)Google Scholar
- 3.The coefficients present in the binomial distribution are the same that appear in the expansion a binomial raised to the
*n*th power, (*a*+*b*)^{n}. A simple iterative way to compute those coefficients is known as Pascal’s triangle. In different countries this triangle is named after different authors, e.g.: the Tartaglia’s triangle in Italy, Yang Hui’s triangle in China, and so on. In particular, the following publications of the triangle are present in literature: • India: published in the tenth century, referring to the work of Pingala, dating back to fifth–second century bc. • Persia: Al-Karaju (953–1029) and Omar Jayyám (1048–1131) • China: Yang Hui (1238–1298); see Fig. 1.8 • Germany: Petrus Apianus (1495–1552) • Italy: Nicolò Fontana Tartaglia (1545) • France: Blaise Pascal (1655)Google Scholar - 4.Yang Hui (杨辉) triangle as published by Zhu Shijie (朱世杰) in
*Siyuan yujian*, (四元玉鉴,*Jade Mirror of the four unknowns*, 1303). Public domain image.Google Scholar - 5.Eadie, W., Drijard, D., James, F., Roos, M., Saudolet, B.: Statistical Methods in Experimental Physics. North Holland, Amsterdam (1971)Google Scholar
- 6.D’Agostini, G.: Bayesian Reasoning in Data Analysis: A Critical Introduction. World Scientific, Hackensack (2003)Google Scholar

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