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hw7_fall10 - ECE 603 Probability and Random Processes Fall...

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Unformatted text preview: ECE 603 - Probability and Random Processes, Fall 2010 Homework #7 Due: 11/19/10, in class 1. A fair die is tossed 100 times: (a) Using Cheybshev’s inequality, find a bound on the probability that the total number of spots (sum of faces that show) is between 316 and 384. (b) Using the Central Limit Theorem, estimate the probability that the total number of spots if between 316 and 384. Compare your answer to part (a). 2. Solve the following problems using the Central Limit Theorem ( intentionally easy and similar to class ): (a) A binary communication makes an error on each bit with probability 0.15. Estimate the proba- bility that more than 20 bit errors are made in 100 bit transmissions. (Can you write down the exact expression for this probability?) (b) The number of messages arriving per second at a switch in a computer network is a Poisson random variable with mean 10 messages/second. Estimate the probability that more than 650 messages arrive in one minute....
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