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Topic: Prob that event A occurs before B...
Replies: 9   Last Post: Jun 25, 2013 5:06 AM

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Registered: 7/12/10
Re: Prob that event A occurs before B...
Posted: Jun 23, 2013 6:08 AM
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On Sunday, June 23, 2013 8:22:33 AM UTC+1, JohnF wrote:
> You're given that two independent events, A and B, will occur
> at some future times. You don't know when they'll occur, but
> you're given two pdf's for that, a(t),b(t),t>=0, with all
> the usual interpretation. What's the prob A occurs before B?
> --

Imagine that the number of times the event can occur is large but finite (N). Solve this case and translate to your continuous case using the usual language of differentials.

Then the probability that you require is p(a(t) = 1 and b(t) < 1) + p(a(t) = 2 and b(t) < 2) ....

This can readily be translated into the language of integrals. The probability that (for example) a(t) = 3 corresponds to a differential -- dx. The probability that b(t) < 3 is a cdf. A large sum corresponds to integration.
Since a cdf is itself an integral, double integrals seem to be involved.

Paul Epstein

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