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!

~ElGreco