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**ElGreco****Guest**

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

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

Hi ElGreco

A counter-example is all you need. If it is not true in one case, it is not true.

And, welcome to the forum!

*Last edited by anonimnystefy (2013-02-02 09:40:08)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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