Consider 5 random variables A,B,C,D and E. E is influenced by C. D is influenced by C and B. B and C are influenced by A. Which of the following statements is not true?

  1. E depends on C
  2. D is independent of A given B and C
  3. B is independent of C given D
  4. E is independent if A given C
  5. C depends on A
  • 1
    $\begingroup$ This appears to be a Mathematics problem rather than a Mathematics puzzle. $\endgroup$ – dcfyj Oct 17 '17 at 18:27

An arrow from $X$ to $Y$ indicates $X$ directly influences $Y$:

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  1. $E$ is influenced by $C$

  2. $D$ is independent of $A|B\land C$

  3. $B$ is independent of $C|D$

  4. $E$ is independent of $A|C$

  5. $C$ depends on $A$

All of the given statements are true.

  • 1
    $\begingroup$ There appears to be an error in your diagram, as D does not directly influence E (according to the question). But I did reach the same conclusion as you - i.e. all the statements are true. $\endgroup$ – Penguino Oct 17 '17 at 21:08
  • $\begingroup$ @Penguino It has been fixed, thanks you for pointing that out. $\endgroup$ – Austin Weaver Oct 17 '17 at 21:21

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