I was wondering, if two random variables are dependent, does that mean that they must be correlated? does one imply on the other or vice versa?
Also, if I know that a joint distribution of two variables is a recognized distribution, say the distribution of $X,Y$ is hyper geometric, does that mean that $X\sim HG$ and $Y\sim HG$? what about the other way?
Let $X$ be $-1$, $0$, or $1$, each with probability $1/3$, and let $Y=X^2$. Then $X$ and $Y$ are uncorrelated, but they are no independed.
Independent random variables for which a correlation exists are always uncorrelated. Their correlation exists only if both of their variances are finite.
I don't know what, if anything, it would mean to say that the joint distribution of two random variables is hypergeometric. The hypergeometric distribution that I know if is a univariate distribution, so $X$ or $Y$ can be hypergeometrically distributed, but the pair $(X,Y)$ cannot.