exam00

# exam00 - THE UNIVERSITY OF CHICAGO Graduate School of...

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THE UNIVERSITY OF CHICAGO Graduate School of Business Business 424-01, Spring Quarter 2000, 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 3 ) 0 be a 3-dimensional Gaussian random variable with mean μ = ( - 3 , 4 , 2) 0 and covariance matrix Σ = 1 0 - 1 0 2 0 - 1 0 2 . Consider the following questions or statements. If the statement is true, brieFy justify it such as citing a result from the textbook. If the statement is false, please explain why. (a) Z 1 + Z 3 is independent of Z 2 . (b) ( Z 1 , Z 3 ) 0 is independent of Z 2 . (c) Consider the simple linear regression model Z 1 = β 0 + β 1 Z 3 + ², where E ( ² ) = 0 and ² is uncorrelated with Z 3 . ±ind the values of β 0 and β 1 . (d) What is the conditional distribution of Z 1 given that Z 3 = 3? (e)

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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.

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exam00 - THE UNIVERSITY OF CHICAGO Graduate School of...

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