Regarding the assumption that $X$ and $Y$ need to be normally jointly distributed, when applying Pearson's correlation test...
what is a good test (function and package) in R to accomplish this task?
In this case, will low "p-values" represent that $X$ and $Y$ have Gaussian bivariate distribution, or the opposite?
CV has already a similar question, but it relies specifically on Matlab solutions.
Although this is a simple question, I think it is a good repository for CV.