W9-slides2 - Lecture 26- Outline and Examples Expectation,...

Info iconThis preview shows pages 1–5. 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

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: 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. 324-325 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. 324-325 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.

Page1 / 10

W9-slides2 - Lecture 26- Outline and Examples Expectation,...

This preview shows document pages 1 - 5. Sign up to view the full document.

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