Re: Question about the problem
- From: "yezi" <ye_line@xxxxxxxxxxx>
- Date: 10 Mar 2006 09:08:10 -0800
Hi:
Suppose I do experiment of shuffle the number from 1, to 10. The
oringinal order of the 1000 numbers are <1,2,3,....10> which Is in
order. The output of the number sequence is sth like
<3,2,1,4,5,9,7,6,8,10>. Then the dlisplacement for abov sequence is
<+2,0 -2,0,0,+3,0,-2,-1,0>
Therefore the
Frequency response of the displacemetn ( F1) is :
+3, 1/10
+2, 1/10
0 , 4/10
-1 , 1/10
-2, 2/10
If we just consider the odd number <1,3,5,7,9> in the sample trial,
then the output sequence is
<3,1,5,9,7>, after reindexing the output sequence, the corresponding
displacement is <+1,-1,0,+1,-1)
The frequency response of the displacement (F2) is:
+1 2/5
0 1/5
-1 2/5
What I am asking is what the relationship between the F1 and F2. Is
possible I just know F1, then I can get the F2. OR vice versa.
If there is some thing misleading, pls let me know.
Thanks for your comments.
C6L1V@xxxxxxx wrote:
yezi wrote:
Hi all:
I have a question with the probability. Suppose there is a sample
space.which is in order like <1,2,3,4,5,7,8,9,...N> Then shuffle the
order the outcome may like< 2,4,1,3,5,6,7,8..N>.What I am caring is the
frequency of out of order .
Your wording is very unclear. Are you asking for probability
distribution of the number of items that are in the wrong position?
Equivalently, are you asking for the distribution of the number in the
right place? If the latter, then for moderate-to-large N (say N greater
than about 10) the distribution of the number in the correct order is
very nearly Poisson with mean 1. The exact distribution is not
difficult to work out, either; it is done in Feller "An Introduction
to Probability Theory and its Applications", Vol. 1---look under the
topic of the "matching problem". Furthermore, without any
approximations, the expected number in the right order is 1 exactly.
This is shown in Ross, "Introduction to Probability Models", but can
also be shown by induction, using the results in Feller.
After done the experiment, there is is a
density function F1 related to a one trial.
What is the density F1 referring to? Anyway, discrete random variables
do not have density functions.
My question If I just caring about the odd number order
<1,3,5,7,9,11...> Then corresponding to those packets, there could be
another density function F2.
What is the relation between the F1 and F2?
I have no idea what you are talking about. Are you asking for the
probability distribution of the number of odd-numbered items that are
in their correct positions (i.e., neglecting the even-numbered items)?
Is that what F2 is supposed to represent?
R.G. Vickson
Adjunct Professor, University of Waterloo
1> My question is How to think about the above question?
2> Which category this problem belong?
Thanks for any idea and comments.
.
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- Question about the problem
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