Determining the correlation

Hi,

I am computing the correlation between two vectors by simply averaging loads of correlation values:

Repeat 100 times:

$\displaystyle Y = X + Noise$, where $\displaystyle Noise$ is AWGN with a normal distribution.

$\displaystyle C = \sigma_{XY}/\sqrt\(\sigma_{X}\sigma_{Y})$

Y and X are vectors of the same length. For my purposes $\displaystyle X$ is just contains known constants.

What I'd like to know is how I can determine the correlation *analytically*?

Thanks.

Re: Determining the correlation

Hey algorithm.

Hint: How do you calculate the covariance and variance analytically?