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ee302hw5_Fa09 - EE302 Homework#5 Assigned Due(by 4:30 in...

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| | Y X Y X | | + 2 2 2 ( ) ( ) EE302 Homework #5 . x y X Y n X Y. X Y n n p y x f y x For each part below, Note: Assigned 10/26/09, Due 11/06/09 (by 4:30 in dropbox in MSEE 330) . 1. A communications satellites is designed to have a mean time to failure of 5 years starting from when it becomes operational. One satellite is in operation at any time. When a satellite fails a new one becomes operational. answer the question for the two cases where (i) failures occurs randomly at continuous times according to a Poisson process; (ii) failures occur randomly at positive integer number of years according to a Bernouilli process. (a) Find the probability that a satellite will last at least 5 years (b) Find the probability that two satellites will last at least 10 years (c) Find the probability that one satellite will last at least 10 years given it lasts at least 5 years. (d) Find the probability that two satellites will last at least 20 years given they last at least 10 years. (e) Find the conditional mean lifetime of one satellite given it lasts at least 5 years.
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