Abstract
In Chapter 5 we again assume Ω is countable and A = 2Ω. A random variable X in this case is defined to be a function from Ω into a set T. A random variable represents an unknown quantity (hence the term variable) that varies not as a variable in an algebraic relation (such as x2 - 9 = 0), but rather varies with the outcome of a random event. Before the random event, we know which values X could possibly assume, but we do not know which one it will take until the random event happens. This is analogous to algebra when we know that x can take on a priori any real value, but we do not know which one (or ones) it will take on until we solve the equation x2 - 9 = 0 (for example).
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© 2000 Springer-Verlag Berlin Heidelberg
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Jacod, J., Protter, P. (2000). Random Variables on a Countable Space. In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51431-9_5
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DOI: https://doi.org/10.1007/978-3-642-51431-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66419-2
Online ISBN: 978-3-642-51431-9
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