Vinh university college of education mathematics department
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MỤC LỤCPREFACE 2 CHAPTER 1: SOME CONCEPTS OF THE PROBABILITY, EXTREMAL FINITE SET THEORY AND THE ENTROPY FUNCTION 1. Some concepts of the probability 1.1.Probability space Throughout this book, Ω denotes a non-empty set of interest, called sample space. For example, Ω is the real line, or Ω is the set of all possible outcomes when tossing a fair coin twice. 1.1.1.Algebra and σ-Algebra Definition: - Let Ω be a non-empty set. A collection F of subsets of Ω is called a algebra over Ω if (i) ; (ii) It is closed under complement: (iii) It is closed under taking finite union: - Let Ω be a non-empty set. A collection F of subsets of Ω is called a σ-field (or σ-algebra) over Ω if (i) ; (ii) It is closed under complement: (iii) It is closed under taking countable unions: 1.1.2.Probability measure Definition: Let be a function. P is called a probability measure if (i) (ii)For every disjoint events then (iii) 1.2. Independence of events Definition 1.2.1. Two events A and B are independent if P(AB) = P(A) · P(B). Proposition1.2.1. Let A and B be events. Let A1 and A2 be events. 1. If A is independent of B, then Ac is independent of B. 2. Suppose and are disjoint. If is independent of B and is independent of B, then is independent of B. Definition 1.2.2. A finite collection of events {A1, A2, . . . , An} are independent if for every I ⊂ {1, 2, . . . , n} we have 1.3. Random variable and distribution function Definition 1.3.1. A random variable is a measurable function on a probability space. Usually, random variables are denoted by capital Roman letters. For example, where µ is the Lesbesgue measure, but it doesn’t really matter. It’s usually Lesbesgue measure. What’s really important is the probability P. For X is called a random vector. tải về 120.21 Kb. Chia sẻ với bạn bè của bạn:
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