# Thread: Number of different randomly produced vectors

1. ## 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

2. ## Re: Number of different randomly produced vectors

Hello,
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 ?

3. ## Re: Number of different randomly produced vectors

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.

4. ## 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...

5. ## Re: Number of different randomly produced vectors

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).