Elements of Probability Theory

Sever Angel Popescu and Marilena Jianu
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Sever Angel Popescu: Technical University of Civil Engineering of Bucharest, Department of Mathematics and Computer Science
Marilena Jianu: Technical University of Civil Engineering of Bucharest, Department of Mathematics and Computer Science

Chapter Chapter 9 in Advanced Mathematics for Engineers and Physicists, 2022, pp 485-609 from Springer

Abstract: Abstract Probability theory is the branch of Mathematics concerned with random phenomena. The modern theory of probability was developed by great mathematicians like: P. Fermat, B. Pascal, J. Bernoulli, P. Laplace, C. F. Gauss, S. D. Poisson, P.L. Chebyshev, A. Markov, A. M. Lyapunov, E. Borel, A. N. Kolmogorov, P. Lévy. In this chapter we make an elementary introduction to probability theory. We present Laplace’s and Kolmogorov’s definitions of probability and show how they can be applied to solve practical problems. We introduce the conditional probability and the Bayes formula, also providing several applications. We define the discrete random variables and the continuous random variables, emphasizing the most used distributions of discrete type (Bernoulli, binomial, Poisson), and of continuous type (normal, gamma, chi-squared, student). We also present the most important limit theorems: the weak law and the strong law of large numbers and the central limit theorem, highlighting the role played by the normal distribution.

Date: 2022
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DOI: 10.1007/978-3-031-21502-5_9

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