EY = E(E(Y|X))
E(Y|X) is the mean of Y conditional on X, which is a function of X. So E(Y|X) is a random variable itself.
If you take expectation again with respect to X, then you will get E(Y).
E(Y|X) is the mean of Y conditional on X, which is a function of X. So E(Y|X) is a random variable itself.
If you take expectation again with respect to X, then you will get E(Y).
根据Introduction to Econometrics 第三版,the mean of Y is the weighted average of the conditional expectation of Y given X, weighted by the probability distribution of X. 比如说,成年人的平均身高等于女性的平均身高乘以女性在人群中的比例,加上男性的平均身高乘以男性在人群中的比例。用数学的方式表达出来就是: