Therefore a random variable can take many dierent

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Unformatted text preview: tably inﬁnite. Axiom P.2 needs to hold only for inﬁnite sets of events that can be listed, or counted. From an engineering perspective, if a set is countably inﬁnite, it means that any element in the set can be represented by a ﬁnite string of bits. The strings for diﬀerent elements of the set can be diﬀerent lengths, but the string for each element is ﬁnite. This could be called a variable length encoding of the set. It is enough to represent the index of the element in the list. For example, if π is the twenty sixth element of the list, then the representation of π would be the binary expansion of 26, or 11010. Proposition 1.5.1 means that it is impossible to index the set of real numbers by variable length binary strings of ﬁnite length. 20 CHAPTER 1. FOUNDATIONS Chapter 2 Discrete-type random variables 2.1 Random variables and probability mass functions Chapter 1 focuses largely on events and their probabilities. An event is closely related to a binary variable; if a probability experiment is performed, then a particular even...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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