Example of Non-Equal Random Variables that are Identically Distributed? What is a simple example of two random variables $X$ and $Y$ that are identically distributed s.t. $X \ne Y$?
Is the only way to achieve this by changing the sample space underneath $X$ and $Y$ (i.e., $\Omega_X \ne \Omega_Y$)?

The most familiar example is for $X$ and $Y$ to be independent. In that case they're non-identically-equal unless $X$ is degenerate.
