L13-ss

# L13-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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5/27/11 Lecture 13 1 STOR 155 Introductory Statistics Lecture 13: Means and Variances of Random Variables The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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5/27/11 Lecture 13 2 Means & Variances of Random Variables • Data – Sample mean: – Sample variance: • Random variable X – Mean: E ( X ) = – Variance: Var ( X ) = E ( X ) and Var ( X ) are summaries of the probability distribution of X . x 2 s 2 X X
5/27/11 Lecture 13 3 Mean of a Discrete Random Variable ( definition )

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5/27/11 Lecture 13 4 Free Throws • A Tar Heel basketball player is a 80% free throw shooter. • Suppose he shoots 10 free throws during each practice. X : number of free throws he makes in a practice. • Find E ( X ).
Lecture 13 5 Free-throws (continued) E ( X ) = 0 P ( X =0) + 1 P ( X =1) + 2 P ( X =2) + … + 10 P ( X =10) = … (by definition ) • Need to compute P ( X = x ) for x =0,1,…, 10. • Any better method ? • Intuition: E ( X ) = 10 (0.8) = 8 • In fact, it’s correct! Why? • Some useful

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L13-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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