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Mathematics, 08.04.2020 05:05 blacee01

Exercise 3. An ambulance travels back and forth, at a constant specific speed v, along a road of length `. We may model the location X of the ambulance at any moment in time to be uniformly distributed over the interval (0, `). Also at any moment in time, an accident (not involving the ambulance itself) occurs at a point uniformly distributed on the road; that is, the location Y of the accident is also uniformly distributed over the interval (0, `). Assume the location of the accident and the location of the ambulance are independent. Supposing the ambulance is capable of immediate U-turns, compute the CDF and PDF of the ambulance’s travel time T to the location of the accident.

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