GaussianAndBinomial

From SGenomics

I've been trying to understand the Gaussian distribution and it's relation to the Binomial distribution. I've kind of decided that the Gaussian distribution is a representation of the Binomial distribution in continuous space. Is this correct?

Anyway, here is some C++ which creates a binomial distribution by adding n random values (-1,0 or 1) to a fixed initial value. I think for this as a kind of 2D random walk. Here's the code:

#include <vector>
#include <iostream>
#include <math.h>

using namespace std;

int main(void) {

  vector<size_t> space(100,0);

  size_t tries=1000000;
  size_t offset=50;
  for(size_t n=0;n<tries;n++) {

    size_t moves=1000;

    int final=50;
    for(size_t t=0;t<moves;t++) {
      int val = rand()%3;
      val -= 1;

      final +=val;
    }
    space[final]++;
  }

  for(int n=0;n<space.size();n++) {
    cout << n << " " << space[n] << endl;
  }

  return 0;
}

Here's the gnuplot generated from the output: