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From: eklhad@ihnet.UUCP (K. A. Dahlke)
Newsgroups: net.math
Subject: Re: Please help: probability problem
Message-ID: <162@ihnet.UUCP>
Date: Fri, 28-Sep-84 17:36:30 EDT
Article-I.D.: ihnet.162
Posted: Fri Sep 28 17:36:30 1984
Date-Received: Sat, 29-Sep-84 09:15:42 EDT
References: <2811@allegra.UUCP>
Organization: AT&T Bell Labs, Naperville, IL
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< munch munch salavate slurp chomp >

	Given the probability of an event completing at time t,
	what is the probability of the last (out of n) events completing
	at time t?

Let me first clarify terms, since they are often used ambiguously.
Let me use the "density" function (p(t)) to indicate the probability
of an event completing near time t.
and the "distribution" function (P(t)) to indicate the probability
of the event completing before time t.
Thus P(t) = integral(x=0,t) p(x).
P(t) starts at 0  and monotonically increases to 1.
I have seen text books use the terms "density" and "distribution" this way,
and two chapters later, describe the distribution of a random variable
with a density function (e.g. uniform distribution:  a nice horizontal line).
But I digress.
At time t1, the event has already completed with probability P(t1).
I am assuming multiple events are independant.
If two events are started together, their times will both be less than t1
with probability P(t1)*P(t1).
Simply raise P(t) to the nth power for n events.
This produces the composite distribution function.
If you need the composite density function, differentiate the result.
You can then use the density function to obtain mean, variance, etc.
-- 

Karl Dahlke    ihnp4!ihnet!eklhad