# Dependence and relationships [closed]

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
• This appears to be a Mathematics problem rather than a Mathematics puzzle. – dcfyj Oct 17 '17 at 18:27

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

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.

• 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. – Penguino Oct 17 '17 at 21:08
• @Penguino It has been fixed, thanks you for pointing that out. – Austin Weaver Oct 17 '17 at 21:21