2010S_FinalExam_4500_Woods - Rensselaer Electrical,...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE-4500 PEA Final Exam May 20, 2010 Closed book - two sheets of notes + calculator allowed Please show work for full credit. Only hand in your answer booklet . Good luck! 1. (10%) A fair die is tossed three times. Given that a 2 appears on the f rst toss, what is the probability of obtaining the sum 7 on the three tosses? 2. (10%) The average number of cars arriving at a tollbooth is λ cars per minute and the probability of cars arriving is assumed to follow the Poisson law. Given that 5 cars arrive in the f rst two minutes, what is the probability of 10 cars arriving in the f rst 4 minutes? 3. (10%) Consider a communication channel corrupted by noise. Let X be the value of the transmitted signal and Y the value of the received signal. Assume that the conditional density of Y given X is Gaussian, that is, f Y | X ( y | x )= 1 2 πσ 2 exp μ ( y x ) 2 2 σ 2 , and that X takes on only the values +1 and
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2010S_FinalExam_4500_Woods - Rensselaer Electrical,...

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