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 ?