Abstract
We shall now take up in earnest the axiomatic treatment sketched in Section 1.3. We assume a sample space Ω, setting a level of description of the realization ω of the system under study. In addition, we postulate that to each numerical-valued observable X(ω) can be attached a number E(X), the expected value or expectation of X. The description of the variation of ω over Ω implied by the specification of these expectations will be termed a probability process or random process. The introduction of a probabilistic element justifies the term random variable, which we shall consistently abbreviate to r.v.
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© 1992 Springer-Verlag New York, Inc.
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Whittle, P. (1992). Expectation. In: Probability via Expectation. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2892-9_2
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DOI: https://doi.org/10.1007/978-1-4612-2892-9_2
Publisher Name: Springer, New York, NY
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