By Fazlollah M. Reza
ISBN-10: 0486682102
ISBN-13: 9780486682105
Info conception
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Extra info for An Introduction to Information Theory
Example text
J. E. , Copenhagen CHAPTER 2 2.. 1. Intuitive Background. Most of us have some elementary intuitive notions about the laws of probability, and we may set up a game or an experiment to test the validity of these notions. This procedure is much like the so-called classical approach to the theory of probability; which was commonly used by mathematicians up to the 1930s. However, this approach has been subjected to considerable criticism; indeed, the literature on the subject contains many contradictions and controversies in the writings of the major authors.
Functions that have numerical values are the most common type. We can define the basic algebraic operations for a family of numerical functions defined over a specific domain X = {x} For instance, iffl(x),f2(x), andf3(x) = const = k have a common domain, 0 fleX) + f2(X) kfl(X), kf2(X) fleX) • f2(X) are also defined over the same domain. 28) DISCRETE SCHEMES WITHOUT MEMORY As a numerical IUIJlctlOD. consider corresnonuence between the of a set a finite number elements and a set of positive integers.
ACU A particular event. A=U The event A must occur (certain) A = 0 The event A is impossible. A' The event A does not occur. x E X or X C A x is any particular outcome of X. The occurrence of x implies the occurrence of A and X. yE A y is not an outcome of the event A. ABC· .. D = S S is the event of the simultaneous occurrence of events D. A+B+C+··· +D=S S is the event of the occurrence of A or B or C or · · · or or any combination of these. ABC · · · D = 0 The events A,B,C, . . , Dare incompatible.
An Introduction to Information Theory by Fazlollah M. Reza
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