2010S_Exam3_WRF - Exam 3, 3pm Thurs May 20 2010 ECSE-2500,...

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Exam 3, 3pm Thurs May 20 2010 ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute Answering 100 of the 130 points is a complete exam. However you have to mark the questions that you don't want graded with a big X across each one. 1. A transmitter is sending a signal to a receiver over a noisy channel, with probability p=1/2. When there is no transmitted signal, the number of photons that the receiver sees is a discrete uniform random variable in the range [0,2]. However, when there is a transmitted signal, the number of photons that the receiver sees is a discrete uniform random variable in the range [1,4]. X is the random variable for the number of photons that the receiver sees. 1. (5) What is P[X=k] for k= 0, 1, 2, 3? 2. (5) What is P[signal present|X=k] for k= 0, 1, 2, 3? 3. (5) What is T, the threshhold value of k for which P[signal present|k] >= 1/2? 4. (5) Pretend that T=1. If you use the decision rule that a signal is present if X>=T, then what is the probability that this rule gives the correct answer?
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2. Students applying to RPI: o Pretend that there are 3,000,000 high school grads this year. o
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2010S_Exam3_WRF - Exam 3, 3pm Thurs May 20 2010 ECSE-2500,...

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