Math Is Fun Forum

ElGreco

Guest

[PROBABILITY] Conditional Independence does not imply Independence

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: 16,049

Re: [PROBABILITY] Conditional Independence does not imply Independence

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)

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