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Probability Theory by Raphael Tavares de Alencar, Marcelo Sampaio de Alencar

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         CHAPTER 4         

RANDOM VARIABLES

The random variable is not a variable, but a function, that is not random at all.

4.1  THE CONCEPT OF A RANDOM VARIABLE

The idea of a random variable has the objective of transposing events of the sample space Ω to Borel segments, or rectangles, in the set of real numbers. This concept is defined informally, by many authors, so that readers can become acquainted with the idea before the appearance of formal applications in the theory.

In reality, what is called a random variable is not a variable, in the strict sense of the word, because it represents a function of random events, that are defined as a result of operations carried out in an algebra of sets. It could be more adequately defined as a dependent ...

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