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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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Paul

Posts: 387
Registered: 7/12/10
Re: Prob that event A occurs before B...
Posted: Jun 24, 2013 4:38 PM
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On Monday, June 24, 2013 3:51:17 PM UTC+1, Ray Vickson wrote:
> On Sunday, June 23, 2013 12:22:33 AM UTC-7, JohnF wrote:
>

> > You're given that two independent events, A and B, will occur
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> >
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> > at some future times. You don't know when they'll occur, but
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> >
>
> > you're given two pdf's for that, a(t),b(t),t>=0, with all
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> >
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> > the usual interpretation. What's the prob A occurs before B?
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> >
>
> > --
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> >
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> > John Forkosh ( mailto: j@f.com where j=john and f=forkosh )
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>
>
> I think you mis-understood what he said and meant; when he said times <= N, I think he meant that you can replace the continuous and unbounded t in a(t) and b(t) by some finite set t_1, r_2, ..., t_N and work with the discrete version of the problem. After doing that, you can pass to the continuous limit.


This is correct about what I meant. Also, the OP's most recent posting does a good job of explaining what was unclear about my initial response. The "event" was indeed an ambiguous expression. I meant "the event that B occurs at a time when A hasn't occurred."

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

By "event" I meant the event to which the above probability applies.

Paul Epstein



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