This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EML 6934 Fall 2009 Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 4 Issued: September 18, 2009, Due: September 25, 2009 (in class) Note: Your work for the questions with [0 pt] are not to be turned in. Problem 1. [5 pt] Show that var ( aX ) = a 2 var ( X ) ( a is a deterministic parameter). Problem 2. [10 + 10 = 20 pt] Prove the CBS (CauchyBunyakovskiiSchwarz) Inequality for random variables. That is, show that for two random variables X and Y , Covar ( X,Y ) radicalbig V ar ( X ) V ar ( Y ) and similarly  E[ XY ]  2 E[ X 2 ]E[ Y 2 ] Problem 3. [10 + 10 = 20 pt] Show the following triangle inequality for random variables, that for two random variables X and Y , radicalbig E[( X + Y ) 2 ] radicalbig E[ X 2 ] + radicalbig E[ Y 2 ] and radicalbig V ar ( X + Y ) radicalbig V ar ( X ) + radicalbig V ar ( Y ) Problem 4 (Sample variance as an estimate of the variance) . [5+10+0 = 15 pt] Let X 1 ,... ,X n be n independent random variables that have the same mean = E[ X i ] and variance 2 = E[( X ) 2 ], and < , 2 < . Now consider the sample mean and the sample variance 2 : = X 1 + X 2 + ...X N N , 2 = ( X 1 ) 2 + ( X 2 ) 2 + + ( X N ) 2...
View
Full
Document
This note was uploaded on 07/03/2011 for the course EML 6934 taught by Professor Staff during the Fall '08 term at University of Florida.
 Fall '08
 Staff

Click to edit the document details