I am asked to give an example for a joint distribution of three random variables, $U$, $V$ and $W$, where $U$ and $V$ are (unconditionally) independent but are NOT conditionally independent given $W$.
It is also known that:
- $U$ and $V$ are normally distributed with a mean of $2$ and a variance of $2$ (that is, $U \sim N(2, 2)$ and $V \sim N(2, 2)$)
- $W$ is a coin toss and has two possible values
I understand the possibility of two independent variables becoming conditionally dependent on a third variable (as well explained on multiple answers of this question for example), but not sure how it applies given the above requirements and would appreciate assistance.
