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Unformatted text preview: Chapter 3: Discrete Random Variables and Probability Distributions Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 1/14 3.1 Discrete Random Variables 1 Random variable; 2 Discrete random variable; Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 2/14 3.2 Probability Distributions and Probability Mass Functions Definition ((Probability) Distribution) In probability theory and statistics, a probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range. Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 3/14 3.2 Probability Distributions and Probability Mass Functions Definition ((Probability) Distribution) In probability theory and statistics, a probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range. Definition (Probability mass function (pmf)) For a discrete random variable X with possible values x 1 , x 2 ,..., x n , a probability mass function is a function such that f ( x i ) ≥ 0; ∑ n i =1 f ( x i ) = 1; f ( x i ) = P ( X = x i ). Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 3/14 Example (315.) x21 1 2 f(x) 1/8 2/8 2/8 2/8 1/8 1 Is f ( x ) is a pmf? Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 4/14 Example (315.) x21 1 2 f(x) 1/8 2/8 2/8 2/8 1/8 1 Is f ( x ) is a pmf? 2 P ( X ≤ 2) Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 4/14 Example (315.) x21 1 2 f(x) 1/8 2/8 2/8 2/8 1/8 1 Is f ( x ) is a pmf? 2 P ( X ≤ 2) 3 P ( X > 2) Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 4/14 Example (315.) x21 1 2 f(x) 1/8 2/8 2/8 2/8 1/8 1 Is f ( x ) is a pmf? 2 P ( X ≤ 2) 3 P ( X > 2) 4 P ( 1 ≤ X ≤ 1) Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 4/14 Example (315.) x21 1 2 f(x) 1/8 2/8 2/8 2/8 1/8 1 Is f ( x ) is a pmf? 2 P ( X ≤ 2) 3 P ( X > 2) 4 P ( 1 ≤ X ≤ 1) 5 P ( X ≤  1 or X = 2) Montgomery&Runger E4; first created on 08/15/08 Compiled on January 20, 2009by Dr. Bin WANG 4/14 Cumulative Distribution Functions Definition (Cumulative Distribution Functions (cdf)) The cumulative distribution function of a discrete random variable...
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This note was uploaded on 02/05/2012 for the course ST 315 taught by Professor Staff during the Fall '11 term at S. Alabama.
 Fall '11
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