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From: Barker.PA@PARC-MAXC.ARPA
Newsgroups: net.physics
Subject: Re:Correction to my Helmut Schmidt article
Message-ID: <16483@sri-arpa.UUCP>
Date: Tue, 7-Feb-84 11:47:00 EST
Article-I.D.: sri-arpa.16483
Posted: Tue Feb  7 11:47:00 1984
Date-Received: Fri, 10-Feb-84 03:16:43 EST
Lines: 60

Lew,


	I have followed this subject with keen interest, I have even obtained a
gieger counter to fool around with. There are a couple of confusiong
points about your last message. First you mention that someone has
stated that the data presented in the graph is movement to the right
above average. However, stasticly average is zero.  If however you mean
the average number of steps away from center in either direction that
number is given by the square root of the number of total steps and is
therefore about 77. Even so the data that I saw  on the nova program was
compared to a curve of random data centered around zero, as if the were
implying that the deviation was away from a random walk that resulted in
no net average displacement.

	I agree with your earlier computer simulation and have generated the
same datsa myself. I have also evaluated the probabilities for a random
walk according to the following formula


		P(X)  =  (1/2)**N*N! / (X!*((NX)/2)!)

where N is total number os steps and P(X) is the prob. of landing on the
Xth step.

which gives the following results,




		  #      P(X)	      total P(all steps below X)

   step= +/-      0     .010300216203     .010300216203
   step= +/-      1     .000000000000     .010300216203
   step= +/-      2     .020593567883     .030893784085
   step= +/-      3     .000000000000     .030893784085
   step= +/-      4     .020572988035     .051466772120
   step= +/-      5     .000000000000     .051466772120
   step= +/-      6     .020538733975     .072005506095
   step= +/-      7     .000000000000     .072005506095
   step= +/-      8     .020490874076     .092496380171
   step= +/-      9     .000000000000     .092496380171


   step= +/-     60     .015261862398     .569012209115
   step= +/-     61     .000000000000     .569012209115


   step= +/-    120     .006205475647     .881743699915
   step= +/-    121     .000000000000     .881743699915


   step= +/-    240     .000169454944     .998139688874



	Points to be made are that there is almost a 12% chance that the data
will come out with a displacement above 120. Not hard to reproduce in a
lab. The chance that it will be beyond 240 is .2 % not 1/10000. 1/10000
is closer to the probability that the displacement is on step # 240 ONLY