Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
From: ludwik kowalski <kowalskil@MAIL.MONTCLAIR.EDU>_______________________________________________
Reply-To: Forum for Physics Educators <PHYS-L@list1.ucc.nau.edu>
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: Average earlier or average later?
Date: Fri, 02 Apr 1976 14:44:47 -0500
On Sep 9, 2005, at 11:43 PM, Bernard Cleyet wrote:
Ludwik!
pse post the source code.
PROGRAM TESTING
!***********************
randomize
let n=1000 ! how many samples from random distr
let meanx=2.2
let stdev=0.5
let sum=0
print "stdev=";stdev
for i=1 to n
call GET_X(mean,stdev,x) ! "measuring" (get x)
let y=x^4 ! calculating from x
let sum=sum+y
next i
let YY=sum/n ! mean from y
print " YY=";YY
end
SUB GET_X(meanx,stdev,x) ! "measuring one x" from
!********************** ! an imposed Gaussian distr
let sum=0
for i=1 to 12
let sum=sum+rnd
next i
let z=sum-6
let x=z*stdev+meanx
end sub
On Sep 9, 2005, at 11:42 AM, Pamela L. Gay wrote:
Okay I'm game for a simulation. Played with excel for 30 seconds and
for
N = 1000
<X_N> = 2.200
stdev(X_N) = 0.374
I found
Y= Sum over N (X_N)^4 / N = 27.499
Y = <X_N>^4 = 23.423
On Sep 9, 2005, at 11:23 AM, ludwik kowalski wrote:
cut
I do not know how wide was the distribution of T in Pamela's
simulation. It turns out, as intuitively expected, that the
discrepancy
between the true Y and the predicted Y grows rapidly when the
distribution of T becomes wider. This is shown below. I am talking
about averaging at the level of Y; averaging at the level of T
produces
a nearly perfect prediction at any standard deviation. Like Pamela, I
used 1000 simulated measurements for each sigma and the mean T=2.2. My
distributions of T were Gaussian.
stdev predicted Y comment
0.0001 23.426 nearly perfect because . . .
0.1 23.71 not a large systematic error . . .
0.25 25.32
0.50 30.25 even larger systematic error due . . .
0.75 42.39 very big systematic error . . .
1.00 60.40 worse