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Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!stolaf!umn-cs!dicomed!dayton!sjm
From: sjm@dayton.UUCP (Steven J. McDowall)
Newsgroups: net.math.stat
Subject: Poisson Summation
Message-ID: <676@dayton.UUCP>
Date: Sun, 26-Jan-86 00:09:06 EST
Article-I.D.: dayton.676
Posted: Sun Jan 26 00:09:06 1986
Date-Received: Tue, 28-Jan-86 05:23:00 EST
Reply-To: sjm@dayton.UUCP (Steven J. McDowall)
Organization: Dayton Hudson Dept. Stores Mpls, MN
Lines: 37
Keywords: poisson , probability, summation

*** For the line eater ***

Ok..I'm working on the following problem for one of my classes,
and can not find/figure out an "easy" way to solve it.

We are given a process that occurs 600 times/hour, and are to
calculate the following probabilities: (The first 2 are easy)

a) That there will be exactly 0 occurences in 3 minutes.
b) That there will be exactly 60 occurences in 3 minutes.

Now for the tough one:
c) If a switch board can handle 20 calls per minute,
that what is the probability that it will be overrun
in 3 minutes with a 600 call/hour poisson distribution?
(Ie: that there will be at least 1 minute with at least
21 calls?)

It seems to me that the way to solve it would be to
calculate SIGMA(P63(3)) (Ie..SUm of the probabilities
of 0-63 events) and subtract 1, giving the probability of
more than 63 events in 3 minutes (which means that we had*
to have 1 minute with more than 21, yes?) However,
*summing* that damn thing is no fun! Especially 63 cases!

By the bye, in case you forget
Pn(t) = [(rt)^n/n!] * e^(-rt)  where r = rate and t = time...n
is the number of occurances exactly*.

Thanks!



-- 
Steven J. McDowall	
Dayton-Hudson Dept. Store. Co.		UUCP: ihnp4!rosevax!dayton!sjm
700 on the Mall				ATT:  1 612 375 2816
Mpls, Mn. 55408