An ambulance travels back and forth, at a constant specific speed v, along a road of length L. We may model the location of the ambulance at any moment in time to be uniformly distributed over the interval (0, L). 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 accidents distance from one of the fixed ends of the road is also uniformly distributed over the interval (0, L). 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 ambulances travel time T to the location of the accident.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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An ambulance travels back and forth, at a constant specific speed v, along a road
of length L. We may model the location of the ambulance at any moment in time
to be uniformly distributed over the interval (0, L). 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 accidents distance from one of the fixed ends
of the road is also uniformly distributed over the interval (0, L). 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 ambulances travel time T to the location of the accident.
Transcribed Image Text:An ambulance travels back and forth, at a constant specific speed v, along a road of length L. We may model the location of the ambulance at any moment in time to be uniformly distributed over the interval (0, L). 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 accidents distance from one of the fixed ends of the road is also uniformly distributed over the interval (0, L). 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 ambulances travel time T to the location of the accident.
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