Abstract
In most practical situations we are not able to fully determine a probability distribution of a random variable or vector under consideration. Nevertheless, we can often obtain partial information on the distribution that suffices for our purpose. The most basic information about the random variable is given by the mean or mathematical expectation and the variance or its square root, which is known as the standard deviation. Other parameters such as higher moments are also considered, but are not as significant so they will be not covered in this book. The substantial role of the mean and variation partially explains the Law of Large Numbers which states convergence of the averages of random variables to their common mean. We will thus discuss these laws as well as various types of convergence of random variables. We will complete this Chapter with a problem on the correlation of two or more random variables.
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© 2002 Springer-Verlag Berlin Heidelberg
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Cyganowski, S., Kloeden, P., Ombach, J. (2002). Parameters of Probability Distributions. In: From Elementary Probability to Stochastic Differential Equations with MAPLE®. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56144-3_4
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DOI: https://doi.org/10.1007/978-3-642-56144-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42666-0
Online ISBN: 978-3-642-56144-3
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