code: private double getExpectedProbability(double x)
      {
          double y = 1 / (standardDeviation * Math.sqrt(Math.PI * 2));
          double z = -(Math.pow(x - mean, 2) / (2 * Math.pow(standardDeviation, 2)));
          return y * Math.exp(z);
      }
docs: This is the probability density function for the Gaussian
  distribution.