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.,
Since statistical methods primarily rely on numerical data, it becomes necessary to represent the outcomes of the sample space mathematically.
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Notes
- 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.
References
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
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Selvamuthu, D., Das, D. (2024). Random Variables and Expectations. In: Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control. University Texts in the Mathematical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-99-9363-5_3
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DOI: https://doi.org/10.1007/978-981-99-9363-5_3
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