assign07 - Stat 351 Fall 2007 Assignment#7 This assignment...

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Stat 351 Fall 2007 Assignment #7 This assignment is due at the beginning of class on Friday, November 9, 2007. You must submit solutions to all problems. As indicated on the course outline, solutions will be graded for both content and clarity of exposition. The solutions that you submit must be neat and orderly. Do not crowd your work or write in multiple columns. Your assignment must be stapled and problem numbers clearly labelled. 1. Suppose that X 1 and X 2 are independent N (0 , 1) random variables. Set Y 1 = X 1 - 3 X 2 + 2 and Y 2 = 2 X 1 - X 2 - 1. (a) Determine the distributions of Y 1 and Y 2 . (b) Determine the distribution of Y = ( Y 1 ,Y 2 ) 0 . 2. Let X have a three-dimensional normal distribution with mean vector μ and covariance matrix Λ given by μ = 3 4 - 3 and Λ = 2 1 3 1 4 - 2 3 - 2 8 , respectively. If Y 1 = X 1 + X 3 and Y 2 = 2 X 2 , determine the distribution of Y = ( Y 1 ,Y 2 ) 0 . 3.
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assign07 - Stat 351 Fall 2007 Assignment#7 This assignment...

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