ch3 - Chapter 3 Discrete Random Variables and Probability...

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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
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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
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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
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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
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Example (3-15.) x -2 -1 0 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
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Example (3-15.) x -2 -1 0 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
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Example (3-15.) x -2 -1 0 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
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Example (3-15.) x -2 -1 0 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
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Example (3-15.) x -2 -1 0 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
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Cumulative Distribution Functions Definition (Cumulative Distribution Functions (cdf)) The cumulative distribution function of a discrete random variable X , denoted as F ( x ), is F ( x ) = P ( X x ) = X x i x f ( x i )
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