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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online