1. (a) Everyone knows correlation is not causation." What is the difference? Present it symbolically, as captured in the potential out-comes model, and explain the meaning of these symbols in plain English.

(b) We know the definition of ATT(Average Treatment Effect on Treated), in symbolic terms in the potential outcomes model. If you had to define "ATU," the average treatment effect on the untreated, also using symbolic terms in the potential outcomes model, how would you do it?

(c) A student who took Stanford's version of PS3 is overheard at a party confidently declaring, "Randomized experiments are necessary for correlation to tell us causal effects such as ATT." How would you explain to this student the inadequacy of Stanford's training on this topic?