ee302hw5_Sp10 - EE302 Homework#5 Assigned Due(by 4:30 in...

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| | +1 = () =1 = kt tk tt t YX EE302 Homework #5 ± }{ } }{² ± } { } | | For each part below, Note: Note: . TK k t h t , Kk T> t a . py x fy x . Assigned 3/10/10, Due 3/26/10 (by 4:30 in dropbox in MSEE 330) . 1. Let and denotethe eventtime andthenumberofevents uptotime respectively for a process which models events which occur at random points in time, (a) Argue that (b) Use part to derive the pmf for a Poisson random variable from the cdf of an Erlang random variable. Hint: 2. Acommunicationssatellitesis designedtohaveameantime tofailureof 5yearsstarting 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 positiveinteger 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
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This note was uploaded on 09/14/2010 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue.

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