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Unformatted text preview: ISyE 2027 Probability with Applications Polly B. He Fall10, Week 12 Reading: Section 9.5, 10.110.2 Propagation of Independence Recall the independence of random variables. Question: Is independence of random variables preserved by functions? Example 9.5.1 Suppose X and Y are two independent random variables with joint distribu tion function F . Define U = 1 { X ∈ ( a,b ] } and V = 1 { Y ∈ ( a,b ] } . Are U and V independent? How would you check? The general rule is called Propagation of Independence . Let X 1 , X 2 , . . . , X n be independent random variables. For each i , let h i : R → R be a function and define the random variable Y i = h i ( X i ) . Then Y 1 , Y 2 , . . . , Y n are independent. ChangeofVariable Formula (Twodimensional) Recall the onedimensional changeofvariable formula: E[ g ( X )] = ∑ i g ( a i ) P ( X = a i ) if X is discrete. What about the twodimensional case?...
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This note was uploaded on 02/21/2011 for the course ISYE 2027 taught by Professor Zahrn during the Fall '08 term at Georgia Tech.
 Fall '08
 Zahrn

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