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I'm trying to understand better the difference between independence and conditional independence.
If I have three independent random variables, X, Y and Z, how could I construct two random variables A and B using X, Y and Z, such as A and B are not independent, but are conditionally independent given Z?
How about $A=X+Z$ and $B=Y+Z$?
($A$ and $B$ are only dependent if $Z$ is not almost surely constant; if it is, there is no solution.)
