3. (BoptsJ Suppose you are interested in the causal effect of smoking (A) on lung cancer (Y). but you are worried about confounding by parents' smoking (U): Children of parents who smoke are more likely to smoke. and are also more likely to develop lung cancer because of secondhand smoking. However, you believe that you can nd a genetic factor (Z) that are (i) causally associated with smoking; iii) independent of parents' smoking behavior; {iii} has no direct effect on lung cancer except for the effect that goes through smoking. {a} (4pts) Draw a DAG that represents this study. {b} (4pts) Find all the ancestors of A in alphabetical order (c) [4pts] Find all the children of A in alphabetical order {d} (4pts) Find all the paths between Z and Y. Which of them are causal paths? Noncausal paths? (e) (4pts) If we want to estimate the causal effect of E on Y, which set of variables shall we adjust for? if} [4pts] Given your DAG. if you know that the association between Z and Y is nonzero. can you use that information to decide if the causal effect of A on Y is zeroinonzero? {g} [4pts] Under your DAG. is it true that the genetic factor (Z) is independent of lung cancer {Y}, conditional on the smoking status (A)? Explain. {h} {3pts} Your collaborator is concerned that the genetic factor may have an direct effect on lung cancer. Draw a DAG to represent their concern. ii} [Spts] Find a statistical test to tell if your collaborator is correct. Hint: nd a set of conditional independence relationship that holds under your DAG. but not under your oollaborator's DAG