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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 lacto-ovo-vegetarian 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 one-way ANOVA model for the data, y ij = + i + ij , ij iid N (0 , 2 ) ....
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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