Concepts of Probability Theory
This approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus.
After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics.
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absolutely continuous assumed autocorrelation function average basic space Bernoulli Bernoulli trials bility boolean function Borel function Borel set chap class of events concept conditional probability consider convergence corresponding deﬁned Deﬁnition density function determined discrete random variable disjoint distribution function elementary outcome elements Example expression fact ﬁrst function FX given ifﬁ iﬁi iﬂi independent class independent random variables index set indicator function inequality integral interval inverse image large numbers law of large Lebesgue Markov mathematical expectation mathematical model mean value minterm moment-generating function mutually exclusive mutually exclusive events nonnegative occurrence P(AB pair partition plane prob proba probability mass distribution probability measure probability theory problem product rule properties random process real line real world real-valued random variable result sample function sequence sigma ﬁeld simple random variables speciﬁc subsets Suppose Theorem tion trials union zero