# Does correlation have to be in the context of (Gaussian) normal distribution?

I am not quite familiar with the concept of correlation. The Pearson's correlation coefficient is defined as:

$\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over \sigma_X\sigma_Y}$

Which makes use of Mean and Standard deviation. But, is it strict to the normal distributed data ? Since Gaussian distribution is configured by mean and variance.

I currently have some which is apparently not following normal distribution. When assessing the correlation between them, is correlation appropriate here ?

• The correlation coefficient exists whenever the relevant expectations exist. Very much not confined to the normal. – André Nicolas Jun 4 '14 at 20:14