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I know this isn't quite

I want to show that conditional independence of $X$ and $Y$ given $Z$ does not imply independence of $X$ and $Y$ (and

So I used coin tosses where:

$X=\{$ first coin tails $\}$

$Y=\{$ second coin tails $\}$

$Z=\{$ both coins same $\}$

I can show that independence does not imply conditional independence.

How do I show that conditional independence does not imply independence?

*advanced*probability, but I'm not sure if I have this right.I want to show that conditional independence of $X$ and $Y$ given $Z$ does not imply independence of $X$ and $Y$ (and

*vice versa*).So I used coin tosses where:

$X=\{$ first coin tails $\}$

$Y=\{$ second coin tails $\}$

$Z=\{$ both coins same $\}$

I can show that independence does not imply conditional independence.

How do I show that conditional independence does not imply independence?

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