Random walk in 3-dimensions problem

Eeezee

Diamond Member
Jul 23, 2005
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I've randomly generated 3-d unit vectors. Basically I had to write a computer program that generated 100 point particles which then took 100 steps or 10000 steps randomly. I had to make a histogram illustrating probability versus R^2 for each of these cases. I am then asked the following question

"Use your histograms if possible to determine whatever you can about the following equation. What is this quantity measuring?

sqrt(average[{R^2 - average(R^2)}^2]) / average(R^2)

So it's one over the average of R^2 multiplied by the square root of the average of the square of R squared minus the average of R squared.

I have little idea what this could be measuring or how to obtain it from a strange looking histogram (it almost looks like a gaussian). I know that the average of R^2 is equal to N, the number of steps,for an ensemble system. I was up until 6AM working on this last night, but now that I'm refreshed after a long night's rest I still have little idea where I'm going with this
 

silverpig

Lifer
Jul 29, 2001
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It looks like a normalized quantity showing the sqrt of the square (to negate the possibility of negatives) of the difference between R^2 and the average value of R^2. So it's kind of like a variance. It's basically asking "How far does a particular measure of R^2 differ from what you would expect to get for R^2?"
 

Born2bwire

Diamond Member
Oct 28, 2005
9,840
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Yeah, it's a normalized variance. So it's basically a weighted measure of the spread of your data, giving a large weight to the walks that did not go very far.
 

Eeezee

Diamond Member
Jul 23, 2005
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Is there anything else that could be said of this? Like, if you were reading a histogram?