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01quiz1 - 1.203J/6.281J/11.526J/13.665J/15.073J/16.76J...

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_______________________________________________________________________ 1.203J/6.281J/11.526J/13.665J/15.073J/16.76J Logistics and Transportation Planning Methods Quiz 1 October 29, 2001 1. Total time allotted is 85 minutes. 2. Please print your name clearly on each page you turn in. 3. Please answer Problems 3 and 4 on a separate page(s) from Problems 1 and 2. Problem 1 (25 points) Suppose that two picks are made from the uniform distribution on (0,a), and let x be the larger of the two. Using Crofton’s method, find E(x 2 ). (HINT: The answer is directly proportional to a 2 .) Problem 2 (25 points) A square city has side 8, and a lower coordinate of (0,0) (and upper coordinate (8,8). It has a horizontal barrier from (0,4) to (4,4), with an opening for traffic at (2,4). Events are uniformly distributed over the city, as is the location of the response vehicle when an event occurs. (The position of the vehicle is independent of the location of the event.) Travel to the event follows grid-distance (Manhattan metric). (i) What is the probability that the presence of the barrier increases the grid distance the vehicle must travel to the event?
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