原文摘抄：

Let x be a random vector that is some function of w, say x =f(w) (The vector x could simply be a subset of w.) This statement implies that if we know the outcome of w, then we know the outcome of x. The most general statement of the LIE: Law of iterated Expecation that we will need is

E(y|x)=E(E(y|w)|x)

In other words, if we write , we can obtain u1(W)=E(y|w) and u2(x)=E(y|x), we can obtain u2(x) by computing the expected value of u2(w) given x: u1(x) =E(u1(w)|x).

问题一：红色的u1(x)和u2(x)是不是有点问题，好像前后逻辑有些问题。是不是u1(x)应当改成u2(x),谢谢？

问题二：请大侠帮我讲讲LIE: Law of Iterated Expectations.能不能介绍一下这个定律或者法则？

问题三：问题二是不是有点类似于求微积分的时候先求外函数然后求内函数？

多谢DX指教了，如果需要我把整本书都传上来吧，不过这个问题好像不用。

文章来源于： Wooldrige, Analysis of cross section and panel data.