I am a bit confused on conditional independence:
Given the following independence assumptions: ⫫, ⫫, ⫫, ⫫|, ⫫|,⫫|
What is the minimal set of independence assumptions needed in order for the equation to be true?
(a) (,) = (|)()
If we know that (,) = (|Y)(), then it must be the case that (|)=(|Y). I am confused as to how knowing conditional probabilities will help with this?
(b) (|) = (|)() Again with this one I know that ()(|) = (,)P(x). Is there any information about X and Y being independent?
Thanks!