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Two distributions

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    "Pat arrives at the bus stop at some time U, which is uniformly distributed between time 0 and time 1, and waits for a bus. The first bus arrives at time T which is exponentially distributed with mean 1/μ. Assume that U and T are independent. What is the probability that Pat catches the first bus?"
    2. Relevant equations & 3. The attempt at a solution

    "Pr {U < T} = [tex]\int[/tex](from 0 to infinity) Pr {U < T | U = s}fU(s) ds"
     
    Last edited: Oct 30, 2008
  2. jcsd
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