03quiz1 - Urban OR Quiz 1 We blew it-Henry Fonda(Easy Rider...

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Urban OR Quiz 1 October 20, 2003 “We blew it.” --Henry Fonda (Easy Rider) Don’t blow it: Just answer all questions, showing all work. Good luck. 1. Suppose that x 1 and x 2 are independent and both U(0,a), and let G(a) be the expected value of the cube of the larger of the two variables. Use Crofton’s method to determine G(a). 2. Suppose that vehicles are distributed over a large city under a spatial Poisson process with parameter λ , and let v i be the straight-line distance to a given point from the i th nearest vehicle to that point. Find the probability that v 4 > 4v 1 and also that v 4 > 2v 2 . (We are referring to the joint event involving v 1 and v 2 , not two separate events.) 3. Mendel arrives at a random time to ride the Lemon Line, on which the intervals between trains are equally like to be 4, 5, and 6 minutes. (i) What is the probability that he waits between 4 and 5 minutes for the next train? (HINT: What is the conditional probability that he waits between 4 and 5 minutes if he arrives in an interval of length X?)
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