Conditional independences given:
- A ⊥ C | B ---------- A and C are independent given B
- D ⊥ B | A, C
- E ⊥ C, D | A
- E ⊥ D | A
and I need to use this information for decomposing the full joint probability P(A, B, C, D, E).
My poor understanding leads me to
P(A, B, C, D, E) = P(B)P(A|B)P(C|B)P(E|A)P(D|A)
However, it does not seem to be correct, as 2. and 3. are just ignored by the answer.
Please kindly shed me some light on the question.
Thank you very much.