1. For two generic random variables Z; and W; the Law of Iterated Expectations (LIE) says that: E\left[W_{i}\right]=E_{Z}\left[E\left[W_{i} \mid Z_{i}\right]\right] E\left[Z_{i}\right]=E_{W}\left[E\left[Z_{i} \mid W_{i}\right]\right] You are given the following regression model:

Y_{i}=\beta_{\mathbf{0}}+\beta_{1} X_{i}+u_{i} and you are told that E[u;|X;] = 0. a) Does A1 hold? b) Is B1 the causal effect of X; on Y;? c) Show that E(u;) = 0. Interpret what it means. d) Show that Cov(ui, X;) = 0. Interpret what it means.