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2024 | OriginalPaper | Chapter

3. Random Variables and Expectations

Authors : Dharmaraja Selvamuthu, Dipayan Das

Published in: Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control

Publisher: Springer Nature Singapore

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Abstract

Random experiments have sample spaces may not consist of numbers. For instance, in a coin-tossing experiment, the sample space consists of the outcomes “head" and “tail”, i.e.,
$$\varOmega =\{\text {head, tail}\}.$$
Since statistical methods primarily rely on numerical data, it becomes necessary to represent the outcomes of the sample space mathematically.

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previous chapter Basic Concepts of Probability
next chapter Standard Distributions
Footnotes
1
Let f be a function from a measurable space \((\varOmega , S)\) into the real numbers. We say that the function is measurable if for each Borel set \(B \in \mathbb {B}\), the set \(\{w\mid f(w) \in B\} \in S\). That is, a real-valued function such that the inverse image of the set of real numbers greater than any given real number is a Borel set.
 
Literature
Castaneda LB, Arunachalam V, Dharmaraja S (2012) Introduction to probability and stochastic processes with applications. Wiley, New York
Ross SM (1998) A first course in probability. Pearson
Metadata
Title
Random Variables and Expectations
Authors
Dharmaraja Selvamuthu
Dipayan Das
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control

Print ISBN: 978-981-9993-62-8

Electronic ISBN: 978-981-9993-63-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-99-9363-5_3

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