UT Knoxville STAT 201  Chapter 18 (63 pages)
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Chapter 18
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 63
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 University of Tennessee
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Chapter 18 Sampling Distribution Models Note A few concepts from Chapter 16 are contained within these slides Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 1 Random Variables A random variable assumes a value based on the outcome of a random event Random variables are denoted by a capital letter such as X Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 2 Discrete Random Variables A discrete random variable is a variable that can take on only whole numbers We denote a particular value that a discrete random variable can take on with a lower case letter such as x Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 3 Discrete Random Variables cont d Examples X the of students that come to class x 27 94 54 X the of people out of 10 that believe in ghosts x 1 7 5 X the of subs sold daily from Subway x X the of goals scored in a MLS game x Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 4 Probability Distribution A probability distribution for a random variable consists of The collection of all possible values of a random variable and the probabilities that the values occur Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 5 Probability Distribution Cont d For a discrete random variable the probability distribution of outcomes is called a probability mass function pmf and is represented with p x A valid pmf must have these characteristics p x 0 for all x p x 1 Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Example Flip a fair coin 5 times X the number of heads x p X x 0 1 2 3 4 5 03 16 31 31 16 03 Is this a valid pmf Chapter18 Presentation 1213 Copyright 2009 Pearson Education Inc 7 Back to the Discrete Random Variables Examples What is expected X the of students that come to class X the of people out of 10 that believe in ghosts X the of subs sold daily from Subway X the of goals scored in a MLS game What value do you expect for each of these examples in the long run on
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