hwk139_6b-S11

hwk139_6b-S11 - not fail for another year? c) If you...

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UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Electrical and Computer Engineering ECE 139 Probability and Statistics Spring 2011 Homework Assignment #6 – Part 2 (Due on Tuesday 5/17/2011 by 8 pm in the Homework Box ) The following are two “ramp-up” and/or review problems to add to homework set #6. They were extracted from prior year exams. Problem # 1 . Many electronic systems have the annoying tendency to only fail catas- trophically once the one year warranty period is over. The lifetime (in years) of some such system is random variable X , satisfying P ( X > x ) = ( 1 x < 1 1 x x 1 a) What is the probability density function of X ? b) If the system has not failed by the end of K years, what is the probability that it will
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Unformatted text preview: not fail for another year? c) If you purchased three such systems (which we assume fail independently) and they are all still working after K years, what is the probability that at least one of them is still working by the end of 2 K years? d) The manufacturer claims that on the average this system works forever. Is this claim laughable or can it be mathematically justied? Problem # 2 . Random variable X has known CDF F X ( x ). a) Let a be a constant and dene the (step) function g ( x ) = u ( x-a ) = ( x &lt; a 1 x a Express E [ g ( X )] in terms of F X ( x ). b) Next let h ( x ) = (-1 x &lt; a 1 x a Express E [ h ( X )] in terms of F X ( x )....
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hwk139_6b-S11 - not fail for another year? c) If you...

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