# Number of different randomly produced vectors

• Nov 6th 2011, 04:36 AM
dudyu
Number of different randomly produced vectors
Hello,

Let X be a descret variable over a variable-space of size k ( $X \in \{ X_1 , X_2 , .. X_k \}$ ).
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
• Nov 6th 2011, 06:22 AM
Moo
Re: Number of different randomly produced vectors
Hello,
Quote:

Originally Posted by dudyu
And let f(X) be a guassian distributionof X's .

What does this sentence mean ? can you be clearer with the problem please ?
• Nov 6th 2011, 07:13 AM
dudyu
Re: Number of different randomly produced vectors
Quote:

Originally Posted by Moo
Hello,

What does this sentence mean ? can you be clearer with the problem please ?

Yes, Sorry
f(X) is a (gaussian) function that describes the probability to get a certain X.
So.. for a vector of length N (N is large..), there will be
$N f $$X_1$$$ occurrences of $X_1$
$N f $$X_2$$$ occurrences of $X_2$
..
and so on.
• Nov 6th 2011, 10:48 AM
Moo
Re: Number of different randomly produced vectors
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...
• Nov 6th 2011, 01:59 PM
dudyu
Re: Number of different randomly produced vectors
Quote:

Originally Posted by Moo
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...

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).