Unformatted text preview: the system to fail is component B. ( b ) The system management needs to install a third component, also connected in a series to the other two components (so that the new system will fail when one of the three components fails). The management can install a component whose lifespan has exponential distribution with the mean x days at a cost C ( x ) = x 1 / 2 for x between . 5 and 10 days. Let T be the lifespan of the new system. Which choice of x will minimize the cost per expected lifetime C ( x ) /ET ? Problem 3 Describe the inverse transform method to generate a sample of continuous random variables with the symmetric Fr´ echet distribution F X ( x ) = b 1 2 ( 1e 1 /x ) if x < 1 2 ( 1 + e1 /x ) if x > . Problem 4 Let X be a Gumbel random variable, i.e. a continuous random variable with a density f X ( x ) = e( x + ex ) ,∞ < x < ∞ . Let Y = X 2 . Find the pdf of Y . 1...
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 Fall '07
 EHRLICHMAN
 Probability distribution, Probability theory, probability density function, World Series, Houston Astros

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