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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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JohnF

Posts: 156
Registered: 5/27/08
Re: Prob that event A occurs before B...
Posted: Jun 23, 2013 9:46 AM
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JohnF <john@please.see.sig.for.email.com> 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?


Thanks, but never mind, I got it. And not sure what
pepstein's talking about, so in case anyone's interested...
Let the cumulative prob be A(t) = int_0^t a(t)dt, and
similarly for B(t). Then G(t) = A(t)(1-B(t)) is the prob
that at or before t, A has occurred and B hasn't,
but that doesn't work as the "kernel" for anything,
which was my original mistake. Instead, a(t)(1-B(t))dt is the prob
that A occurs between t and t+dt, and that B hasn't occurred
yet. So just integrate that, P_ab = int_0^infty a(t)(1-B(t))dt.
And note how P_ba = 1-P_ab.
--
John Forkosh ( mailto: j@f.com where j=john and f=forkosh )



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