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hw3 - EE 351K Probability Statistics and Random Processes...

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EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 3 Due Wednesday, February 18th 2009 Problem 1 You are visiting the rainforest, but unfortunately your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.5. If a mosquito lands, it will bite you with probability 0.3, and it will never bother you with probability 0.7, independently of other mosquitoes. What is the expected time between successive bites? Problem 2 Let X 1 , ..., X n be independent, identically distributed random variables with common mean and variance. Find the values of c and d that will make the following formula true: E [( X 1 + .... + X n ) 2 ] = c ( E [ X 1 ]) 2 + dE [( X 1 ) 2 ] . Problem 3 A class of n students takes a test in which each student gets an A with probability p , a B with probability q , and a grade below B with probability 1 - p - q , independently of any other student. If X and Y
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