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HW3_Spring11

# HW3_Spring11 - ELEC210 Spring 2011 Homework-3 1 Let be the...

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ELEC210 Spring 2011 Homework-3 1. Let ܺ be the maximum of the number of heads obtained when Carlos and Michael each flip a fair coin twice. a) Describe the underlying space ܵ of this random experiment and specify the probabilities of its elementary events. b) Show the mapping from ܵ to ܵ , the range of ܺ . c) Find the probabilities for the various values of ܺ . d) Compare the pmf of ܺ with the pmf of ܻ , the number of heads in two tosses of a fair coin. Explain the difference. e) Suppose that Carlos uses a coin with probabilities of heads ݌ = 3/4 . Find the pmf of ܺ . 2. A modem transmits a +2 voltage signal into a channel. The channel adds to this signal a noise term that is drawn from the set {0, −1, −2, −3} with respective probabilities { ଵ଴ , ଵ଴ , ଵ଴ , ଵ଴ } . a) Find the pmf of the output ܻ of the channel. b) What is the probability that the output of the channel is equal to the input of the channel?

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