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464 Midterm1 DEN

# 464 Midterm1 DEN - EE 464 Midterm Exam Oct 15 2009...

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EE 464 Midterm Exam Oct. 15, 2009 12:30pm-1:50pm Name: ID Number: Remote Location(Den students): Instructions: This is a close book exam. You are not allowed to use books, notes and computers, but allowed to bring in 1 crib sheet and calculators. Write your name, remote location and ID number in the space provided before start. The maximum score is 100 points. Prob. Max. Score Your Score 1 15 2 50 3 25 4 25 5 45 total 160 1

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Problem 1. (15 points) There are 5 white and 5 black balls. Take randomly 4 balls and put in an urn. Pick 1 ball from the urn randomly. If this ball is black, what is the probability that the number of black balls remained in the urn is 0, 1, 2 ,3 ? Without replacement, if pick 1 more ball, what is the probability that this ball is white? 2
Problem 2. 2.1) (25 points) Let F X ( x ) , F Y ( y ) be the probability distribution functions of two indepen- dent random variables X and Y respectively. Write down the probability distribution functions of ˜ X 1 = max { X, Y } and ˜ X 2 = min { X, Y } . Let f X ( x ) = λe - λx , f Y ( y ) = βe - βy ,

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464 Midterm1 DEN - EE 464 Midterm Exam Oct 15 2009...

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