Finding a Factor's Contribution to An Average of a Product

  • Context: Undergrad 
  • Thread starter Thread starter Spanky1996
  • Start date Start date
  • Tags Tags
    Average Product
Click For Summary

Discussion Overview

The discussion revolves around understanding the contribution of a specific factor (A) in an ensemble average of a product involving random variables A, B, and C. Participants explore the implications of defining the contribution of A and the characteristics of the random variables involved, including their independence and distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to define the contribution of A in the average X and whether this contribution is obscured in the ensemble average.
  • Another participant emphasizes the importance of defining the variables and understanding their probability distributions, particularly questioning their independence.
  • There is a suggestion to use Monte Carlo simulations to analyze the random variables, with a specific mention of creating histograms and comparing averages and standard deviations.
  • A participant expresses uncertainty about how to define the role of A in the final average X and seeks clarification on a specific Excel function mentioned in the discussion.
  • Further inquiries are made about the characteristics of the random variables, such as their second moments, positivity, and boundedness.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to define the contribution of A or the implications of the random variables' characteristics. Multiple viewpoints and questions remain unresolved.

Contextual Notes

Participants note the importance of defining the variables clearly and understanding their distributions, but there are limitations in the discussion regarding the assumptions about independence and the specific characteristics of the random variables.

Who May Find This Useful

This discussion may be useful for individuals interested in statistical analysis, Monte Carlo simulations, and the behavior of random variables in ensemble averages.

Spanky1996
Messages
7
Reaction score
0
Say that there is an object

[tex]X = <ABC> = (A_1B_1C_1+A_2B_2C_2+...+A_NB_NC_N)/N[/tex]

Is there any way to say what [tex]X_A[/tex] is? Or what exactly the A term in all of these terms contributed to X? Or is that info pretty much washed out in this type of ensemble average?

Oh, and A, B and C are random values. I will say, in my problem they do differ by about an order of magnitude from each other.

Thanks for any insights.
 
Last edited:
Physics news on Phys.org
Spanky1996 said:
Is there any way to say what ##X_A## is
First you have to define it ...

Next you are interested in the probability distributions of your stochastic variables. Are the variables independent ?

Spanky1996 said:
they do differ by about an order of magnitude from each other
I think that's less interesting: you can divide each variable by a scale factor without doing much damage.

It's fun playing with Monte Carlo's in Excel: make three columns of a thousand ' =rand() ' cells each and make a histogram of the products
Look at average and stdev for each column
Compare with ' =rand() - 0.5 '
 
  • Like
Likes   Reactions: Spanky1996
BvU said:
First you have to define it ...

Next you are interested in the probability distributions of your stochastic variables. Are the variables independent ?I think that's less interesting: you can divide each variable by a scale factor without doing much damage.

It's fun playing with Monte Carlo's in Excel: make three columns of a thousand ' =rand() ' cells each and make a histogram of the products
Look at average and stdev for each column
Compare with ' =rand() - 0.5 '
I am actually doing monte Carlo simulations, bravo.

I guess defining it is my issue. I'm not sure how one can define/examine what role the set of A's had in whatever the final answer is for X.

The variables are independent.

I was thinking of doing something similar to what you suggest in your last paragraph. I don't understand the last bit though '=rand()-0.5' what is that?

Thank you for your interest!
 
Spanky1996 said:
'=rand()-0.5' what is that
Gives a different average (of course) and sigma (!) and a different histogram :smile:
 
what else can you tell us about these random variables-- Is there a second moment?

also I typically wonder: are they positive valued? are they bounded?
 

Similar threads

Undergrad Averages and average speed/instantaneous speed relation
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Average of prime factors growth
  • · Replies 12 ·
Replies
12
Views
2K
High School Death Rally: an intricate probability problem?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What is the correct definition of measurement uncertainty?
  • · Replies 21 ·
Replies
21
Views
3K
Graduate What are your insights on The Hardest Logic Puzzle Ever?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Equivalence of 2 definitions of the magnitude of the cross product?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Progress In Calculating The HLbL Contribution To Muon g-2
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad Two-body correlation function computation
  • · Replies 1 ·
Replies
1
Views
3K
Use Remainder theorem to find factors of ##(a-b)^3+(b-c)^3+(c-a)^3##
  • · Replies 4 ·
Replies
4
Views
2K
Find the coefficient of the 1996th term of a product
  • · Replies 3 ·
Replies
3
Views
2K