Question: Spatio-Temporal Poisson Process problem On 1-94, from Ann Arbor to Detroit, accidents happen on the rush hour from 8 AM to 9 AM according to

Spatio-Temporal Poisson Process problem

On 1-94, from Ann Arbor to Detroit, accidents happen on the rush hour from 8 AM to 9 AM according to a spatio-temporal Poisson process with intensity 1 = 2. Assume that the Poisson process is space-time homogeneous. Assume that the distance between Ann Arbor and Detroit is 60 distance units. Time is measured in minutes. Assume that there are no accidents on 1-94 before 8 AM. You start driving from Ann Arbor at 8 AM to Detroit with speed 1 distance unit per time unit. Let T denote the time to see the first accident. Find the PDF of T

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