Number of different randomly produced vectors

Hello,

Let X be a descret variable over a variable-space of size k ( $\displaystyle X \in \{ X_1 , X_2 , .. X_k \}$ ).

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

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 ?

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

$\displaystyle N f \( X_1 \)$ occurrences of $\displaystyle X_1$

$\displaystyle N f \( X_2 \)$ occurrences of $\displaystyle X_2$

..

and so on.

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...

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...

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).