lecturenotesweek12

lecturenotesweek12 - ISyE 2027 Probability with...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ISyE 2027 Probability with Applications Polly B. He Fall10, Week 12 Reading: Section 9.5, 10.1-10.2 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. Change-of-Variable Formula (Two-dimensional) Recall the one-dimensional change-of-variable formula: E[ g ( X )] = ∑ i g ( a i ) P ( X = a i ) if X is discrete. What about the two-dimensional case?...
View Full Document

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.

Page1 / 4

lecturenotesweek12 - ISyE 2027 Probability with...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online