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

[Spanky1996]

Say that there is an object

$$X = <ABC> = (A_1B_1C_1+A_2B_2C_2+...+A_NB_NC_N)/N$$

Is there any way to say what $$X_A$$ 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.

 

[BvU]

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 ?

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 '

 

[Spanky1996]

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!

 

[BvU]

'=rand()-0.5' what is that

Gives a different average (of course) and sigma (!) and a different histogram

 

[StoneTemplePython]

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?