From - Mon Aug 17 18:41:02 1998
From: horst.kraemer@snafu.de (Horst Kraemer)
Newsgroups: sci.stat.math
Subject: Re: classical poisson process problem
Date: Mon, 17 Aug 1998 14:28:21 GMT
Message-ID: <35d7fd94.341134614@news.snafu.de>
References: <6r2vr1$f0q$1@lwnws01.ne.highway1.com>
Lines: 62
On Fri, 14 Aug 1998 23:38:09 -0400, "Arthur M. Schneiderman"
wrote:
>Trains arrive randomly at a station at an average rate of 1 per x minutes
> or y per hour).
>
>(a) You arrive at the station and there is no train in sight. What is the
>probability that the next train arrives in T minutes?
>
>(b) You arrive at the station just as a train pulls away. Now what is the
>answer to (a).
>
>I remember this question on an exam I took 20 years ago. I also remember
>that I got it wrong and didn't understand why. What I do remember is that
>(b) considers the conditional probability given that the event just
>occurred. Can anyone help me? Can anyone give me a reference?
>
>PS. No, it hasn't kept me up for 20 years. I need to know the answer for a
>similar problem that I'm working on.
By definition a process is a POISSON point process with intensity m
(in your case for example m = 10, 10 trains per hour, the unit if T is
"hours") if the probability that there are exactly k events (arrivals)
in any interval [t0,t0+T] has a POISSON distribution with mean T*m.
(mT)^k
Pr(k) = ------- * exp (-mT)
k!
This distribution is the same for any t0 and any T>=0 and the
distributions for disjoint time intervals [t0,t1], [t2,t3], t1