pmrdk

05-11-2010, 02:05 PM

Hi!

I wish to do the following:

I have two vectors with N elements in each. All elements are set to zero.

Now, in each vector I select n indices at random and set the corresponding elements to 1.

My goal is to calculate the expected overlap between the vectors as a function of n. That is, how many elements have 1 in both vectors.

Initially I thought about using the binomial distribution with probability p=(n/N)*(n/N), but clearly this is incorrect, since we have the constraint that only n elements should have the value 1. Therefore we have not n independent trails. I also cannot apply the hyper-geometric distribution directly, since we consider two random variables.

Any thoughts? :confused:

I wish to do the following:

I have two vectors with N elements in each. All elements are set to zero.

Now, in each vector I select n indices at random and set the corresponding elements to 1.

My goal is to calculate the expected overlap between the vectors as a function of n. That is, how many elements have 1 in both vectors.

Initially I thought about using the binomial distribution with probability p=(n/N)*(n/N), but clearly this is incorrect, since we have the constraint that only n elements should have the value 1. Therefore we have not n independent trails. I also cannot apply the hyper-geometric distribution directly, since we consider two random variables.

Any thoughts? :confused: