MIT 6 041 - Quiz 2 (6 pages)

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Quiz 2



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Quiz 2

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Problems/Exams


Pages:
6
School:
Massachusetts Institute of Technology
Course:
6 041 - Probabilistic Systems Analysis and Applied Probability
Probabilistic Systems Analysis and Applied Probability Documents

Unformatted text preview:

6 041 6 431 Spring 2008 Quiz 2 Wednesday April 16 7 30 9 30 PM DO NOT TURN THIS PAGE OVER UNTIL YOU ARE TOLD TO DO SO Name Question 0 1 2 Recitation Instructor TA 3 6 041 6 431 Part Score all a b c d e f a b c d e Total Out of 3 36 4 5 5 8 5 6 4 6 6 6 6 100 Write your solutions in this quiz packet only solutions in the quiz packet will be graded Question one multiple choice questions will receive no partial credit Partial credit for question two and three will be awarded You are allowed 2 two sided 8 5 by 11 formula sheet plus a calculator You have 120 minutes to complete the quiz Be neat You will not get credit if we can t read it We will send out an email with more information on how to obtain your quiz before drop date Good Luck Massachusetts Institute of Technology Department of Electrical Engineering Computer Science 6 041 6 431 Probabilistic Systems Analysis Spring 2008 Question 1 Multiple choice questions CLEARLY circle the best answer for each question below Each question is worth 4 points each with no partial credit given a 4 pts Let X1 X2 and X3 be independent random variables with the continuous uniform distribution over 0 1 Then P X1 X2 X3 i 1 6 ii 1 3 iii 1 2 iv 1 4 b 4 pts Let X and Y be two continuous random variables Then i E XY E X E Y ii E X 2 Y 2 E X 2 E Y 2 iii fX Y x y fX x fY y iv var X Y var X var Y c 4 pts Suppose X is uniformly distributed over 0 4 and Y is uniformly distributed over 0 1 Assume X and Y are independent Let Z X Y Then i fZ 4 5 0 ii fZ 4 5 1 8 iii fZ 4 5 1 4 iv fZ 4 5 1 2 d 4 pts For the random variables de ned in part c P max X Y 3 is equal to i 0 ii 9 4 iii 3 4 iv 1 4 e 4 pts Consider the following variant of the hat problem from lecture N people put their hats in a closet at the start of a party where each hat is uniquely identi ed At the end of the party each person randomly selects a hat from the closet Suppose N is a Poisson random variable with parameter If X is the number of people who pick their own hats then E X is



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