Question 1 (30 points) Consider a binary treatment variable A E {0, 1} and a continuous mediator M. X denotes the baseline covariates. Prove why the following equation holds using the identification assumptions we learned: E(Y1.MO 1" _you" [X) = E(Y | 4 = 1, M = m, X) - E(Y | A = 0, M = m, X) }dFMJA O,x(m) [Hint ]] The following conditions should be used: for all levels of a, a', m, yam JI A| X; yam I M" | X, A; Ma IL A | X, and consistency. Please specify when each of this condition is used in your proof. [Hint 2] Use the following condition as well: yom JI A | Mo' = m', X for all levels of a, a', m, m