Hello,
Let X be a descret variable over a variable-space of size k ( ).
And let f(X) be a guassian distributionof X's .
I am randomly choosing an X using disribution f(X), and repeat this processes N times, until I get a vector of size N. (N > k, and can be N >> k if it will make the problem easyer..).
My question is:
Is there a way to estimate how many different such vectors I can get from this process?
Thank you
It's still not clear (for gaussian function yes, but not the rest). Do you have the exact wording of the problem somewhere ?
I think there's also a confusion with capital X and small x, and with the wording itself...
Hey, thanks for your interest.
There's no exact wording, but here's a pseudo-code of the algorithem I'm running:
- Set vector v = [] (empty)
do the following 10^6 times: {
- Randomly choose one number from the set { 0 , 1 , 2 , .. , 1000 } using distribuition f(X).
- Append the chosen number to vector v
}
At the end of this process, I have a vector of size 10^6.
I want to know how many different vectors I can *actually* get from this process.
By "actually" I mean- because of the gaussian disribution, there's almost no chance I'll get a vector which is all 1's: (1,1,1,1,...1).
so this, of example, is a vector I don't want to count.
I know that this problem is not very well defined, that's why I'm asking for an estimation of the number. Either that, or.. I can try to well-define it:
For instance, lets say I want to count only vectors I have more than M% probabilty of getting in this process, (where M is a certain number you can decide on).