Does Pearson correlation coefficient implicitely assume that random variables are Normaly distributed?

Question

I have two related questions:

1- Does Pearson correlation coefficient of two random variables, implicitly assume that random variables (X,Y) are Normally distributed (according to normal distribution)?

2- If we have this knowledge that two random variables X and Y are distributed according to a distribution other than Normal, e.g., Beta, is it still acceptable to measure the association between these two random variables with Pearson?

Answer 1

No, it's simply the standardized second mixed moment (covariance).

If you imbue it with distributional assumptions, however, you can derive statistics for hypothesis tests. That's where normality assumptions will often show up.