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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 justiﬁed? Problem # 2 . Random variable X has known CDF F X ( x ). a) Let a be a constant and deﬁne the (step) function g ( x ) = u ( x-a ) = ( x < a 1 x ≥ a Express E [ g ( X )] in terms of F X ( x ). b) Next let h ( x ) = (-1 x < a 1 x ≥ a Express E [ h ( X )] in terms of F X ( x )....
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- Spring '08
- Probability distribution, Probability theory, probability density function, Cumulative distribution function, cdf FX