This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 26 Outline and Examples Expectation, Covariance, Variance and Correlation (Ross § 7.4) Three properties of Variance: Property V1: Computational formula for Variance. Var( X ) = E ( X 2 ) [ E ( X )] 2 . Property V2: Scaling and Shifting. Var( aX + b ) = a 2 Var( X ). Property V3: Var( b ) = 0 for any constant b . Var( X ) = 0 if and only if P ( X = μ ) = 1. Example. Ex 4a p. 324325 Let X 1 ,..., X n be independent and identically distributed random variables having expected value μ and variance σ 2 . Let ¯ X = P n i =1 X i n be the sample mean. The quantities X i ¯ X , i = 1 ,..., n are called deviations , as they equal the differences between the individual data and the sample mean. The random variable S 2 = n X i =1 ( X i ¯ X ) 2 n 1 is called the sample variance . Find (a) Var( ¯ X ) and (b) E [ S 2 ]. Solution. Example. Ex 4a p. 324325 Let X 1 ,..., X n be independent and identically distributed random variables having expected value μ and variance σ 2 . Let....
View
Full
Document
This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.
 Spring '10
 RohiniKumar
 Correlation, Covariance, Variance

Click to edit the document details