# Homework Help: Two distributions

1. Oct 30, 2008

### Travis Cooper

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} = $$\int$$(from 0 to infinity) Pr {U < T | U = s}fU(s) ds"

Last edited: Oct 30, 2008