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Unformatted text preview: 1 Sixth Problem Assignment EECS 401 Problem 1 An ambulance travels back and forth, at a constant speed, along a road of length L . At a certain moment of time an accident occurs at a point uniformly dis tributed on the road. (That is, its distance from one of the fixed ends of the road is uniformly distributed over ( 0, L ) .) Assuming that the ambulance’s location at the mo ment of the accident is also uniformly distributed, compute, assuming independence, the distribution of its distance from the accident. Problem 2 Let X 1 , X 2 and X 3 be three independent, continuous random variables with the same distribution. Given that X 2 is smaller than X 3 , what is the conditional probability that X 1 is smaller than X 2 ? Problem 3 Random variables X and Y are described by the joint PDF f X,Y ( x, y ) = 1, if 0 ♼ x ♼ 1, 0 ♼ y ♼ 1 0, otherwise and random variable Z is defined by Z = XY ....
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 Spring '08
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 Variance, Probability theory, probability density function

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