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"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?"

This is not a homework problem but a practice problem in the text which no answer is supplied for. I have the following integral:

Pr {U < T} = *Integral from 0 to infinity* Pr {U < T | U = s}f

Please tell me how I can solve these kinds of problems.

This is not a homework problem but a practice problem in the text which no answer is supplied for. I have the following integral:

Pr {U < T} = *Integral from 0 to infinity* Pr {U < T | U = s}f

_{U}(s) dsPlease tell me how I can solve these kinds of problems.

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