I was wondering about the following:
Let's say we have two random variables $X,Y$ that obey both Poisson's distribution. Now, if we take $X=Y$ then they are clearly dependent. But what happens if we say that $X$ and $Y$ are Poisson distributions with different parameters $\lambda_x \neq \lambda_y$?
Does this mean, that they are independent?
If this is not true: Is it true for any distribution, that if you have random variables with different parameters, then they are automotically independent?