# Linked Questions

1answer
6k views

### iterated expectation conditional on two variables

How to prove that $E[Y]=E[E[E[Y|X_1, X_2]]]$ ? PS. I don't see how $E[E(Y|X_{1},X_{2})|X_{1}]=Y[Y|X_{1}]$ and $E[Y]=E[E(Y|X_{1})]$ can be used here. But it feels close. Please help, I'm stuck PPS. ...
1answer
1k views

1answer
861 views

### Covariance of Poisson and Conditional Binomial RV's

Problem Statement Let $X$ and $Y$ be random variables such that $X \sim \text{Poisson}(\lambda)$ and $Y|X \sim \text{Binomial}(x+1,p)$. Find $\text{Cov(X,Y)}$. Attempt at a Solution I would like to ...
1answer
794 views

### Are the law of iterated expectation and the law of total expectations the same?

On the Wikipedia page of the Law of total expectations it is said that The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, ...
2answers
447 views

### Is this formula for the Law of Iterated Expectations correct?

I saw two versions of the law of iterated expectations, this one: \begin{align} E(E(Y\vert X)) = E(Y) \end{align} and this one: \begin{align} E(E(Y\vert X_1, X_2)\vert X_1) = E(Y \vert X_1) \end{align}...
1answer
476 views

### Implications of strict exogeneity for OLS in time series

Zero Conditional Mean (ZCM), or Strict Exogeneity, is given by: $E[u|X]=0$ Equivalently, $E[u_t|X]=0, t=1,...,T$ Is it true that this implies: Zero Unconditional Mean: $E[u_t]=0, \forall t$ ...
1answer
255 views