Hello everybody, I have a probability question.
Could you please help me prove that "Conditional Independence does not imply Independence", and vice-versa "(Absolute) Independence does not imply Conditional Independence"?
Every book and online resource seems to take it for granted. They only offer simple counter examples, but I haven't found a formal proof, e.g., by contradiction.
If you can reference a book chapter or post the basics of the proof(s) it would help a lot :-)
Thank you for your time!