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: STAT424 Spring 2010 Homework #3 Feb 23, 2010 Homework 3 Due: Tuesday, March 2, 2010 1) Another example for marginally normally distributed and uncorrelated do not imply inde pendent . Suppose X N (0 , 1). Then generate the other random variable Y by tossing a fair coin: let Y = X if we observe a head, otherwise Y = X . In other words, Y = WX, where W = 1 with prob 1 / 2 , 1 with prob 1 / 2 . (a) Show that Y N (0 , 1). (b) Show that X and Y are uncorrelated. (c) Show that X and Y are not independent, which, consequently, implies that jointly X and Y do not follow a normal distribution. Hint: check whether P ( Y > 2  X = 2) = P ( Y > 2). 2) Researchers compared protein intake among three groups of postmenopausal women. The mean and sample standard deviation of protein intake as well as the group sizes are presented in the table below: Group Mean SD Group Size Women eating a standard American diet (SRD) 75 9 10 Women eating a lactoovovegetarian diet (LAC) 57 13 10 Women eating a strict vegetarian diet (VEG) 48 17 10 where Mean i = y i , SD i = h 1 n i 1 n i X j =1 ( y ij y i ) 2 i 1 / 2 . Consider a oneway ANOVA model for the data, y ij = + i + ij , ij iid N (0 , 2 ) ....
View
Full
Document
This note was uploaded on 10/24/2010 for the course STAT 424 taught by Professor Liang,f during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Liang,F
 Variance

Click to edit the document details