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Unformatted text preview: THE UNIVERSITY OF CHICAGO Graduate School of Business Business 424-01, Spring Quarter 1998, Mr. Ruey S. Tsay Mid-term Exam Notes : 1. Open book and notes. The exam time is 80 minutes. 2. Write your answers in a bluebook. Mark the solution clearly. 1. Let Z = ( Z 1 ,Z 2 , ,Z m ) be a m-dimensional Gaussian random variable with mean = ( 1 , 2 , , m ) and a positive definite covariance matrix = ( ij ). Consider the following questions or statements. If the statement is true, briefly justify it such as citing a result from the textbook. If the statement is false, please explain why. (a) ( Z- ) - 1 ( Z- ) has a (central) chi-square distribution with m degrees of freedom. (b) The conditional distribution of Z 1 , given Z 2 = z 2 is normal with mean 1 + 12 22 ( z 2- 2 ) and variance 11 + 2 12 2 2 . (c) Consider the simple linear regression model Z 1 = + 1 Z 2 + ....
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This note was uploaded on 12/16/2011 for the course STAT 5705 taught by Professor Staff during the Fall '09 term at FSU.
- Fall '09