JohnF
Posts:
165
Registered:
5/27/08


Re: Prob that event A occurs before B...
Posted:
Jun 23, 2013 9:46 AM


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)(1B(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)(1B(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)(1B(t))dt. And note how P_ba = 1P_ab.  John Forkosh ( mailto: j@f.com where j=john and f=forkosh )

