Final-Fall2007-08-John-Haddad

Final-Fall2007-08-John-Haddad - AMERICAN UNIVERSITY of...

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Unformatted text preview: AMERICAN UNIVERSITY of BEIRUT STAT 230, Final Examination Time = 1 hour and 30 minutes Jan 25, 2008 You are allowed to use a calculator, one formula sheet, tables of discrete and continuous distributions. (GOOD LUCK!) 1. Consider the experiment of rolling a pair of fair 4-sided dice. Let X 1 be the outcome on die 1 , and X 2 be the outcome on die 2 respec- tively. Define Y 1 = max { X 1 , X 2 } and Y 2 = | X 1- X 2 | . Determine the Covariance of Y 1 and Y 2 . [15 pts] 2. Let the joint pdf of the two random variables X and Y be f ( x, y ) = kx if 0 < x < y < 1, 0 elsewhere, and k is a positive constant. (a) Find the value of k such that f ( x, y ) is a joint pdf . [5 pts] (b) Determine the marginal pdf of X , f 1 ( x ), and the marginal pdf of Y , f 2 ( y ), respectively. [10 pts] (c) Are the random variables X and Y independent? [5 pts] 3. Let X 1 and X 2 be a random sample of size 2 from the standard normal distribution. Let Y 1 = ( X 1 + X 2 ) / √ 2 and Y 2 = ( X 1- X 2 ) / √ 2. Show2....
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This note was uploaded on 03/01/2010 for the course STAT 230 taught by Professor Variousteachers during the Spring '10 term at American University of Beirut.

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Final-Fall2007-08-John-Haddad - AMERICAN UNIVERSITY of...

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