Linked Questions
10 questions linked to/from A generalization of the Law of Iterated Expectations
2
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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. ...
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5
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1
answer
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Exact meaning of conditional expectation $\mathbb{E}[X|\mathcal{F}]$
I'm going through elementary literature on measure theory from Shreve (Vol II) and having a hard interpreting the meaning of $\mathbb{E}[X|\mathcal{F(t)}]$ where $X$ is a random variable and $\mathcal{...
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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, ...
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3
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2
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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}...
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3
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2
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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 ...
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-1
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1
answer
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Law of iterated expectations for several variables
There are tons of questions related to the LIE, but all the ones I've seen do not help in my case, including this one and this one.
I know that by Law of Iterated Expectations (LIE), $E(x_{i}|A_{i})=...
- 2,746
0
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1
answer
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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: $E[u_t]=0, \forall t$
...
- 13
2
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1
answer
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Proving for an AR(2) process that $E[X_t | F_{t-1}]=E[X_t | F_{t-2}]=E[X_t | F_{t-3}]$
An exercise states:
Using the law of iterated expectations applied to an AR(2) process, verify that
$E_{t−k} . . . E_{t−1} (X_t ) = E(X_t |F_{t−k} ) $ for $ k = 1, 2, 3 $ where $ E_{t−k} (X_t ) = E(...
- 1,465
1
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1
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Conditional Expectation with two random variables
I know $E[E[x\mid y]] = E[x]$ by smoothing property of the expectations. Then, I came across the following equation:
In this equation we have:
$$E[E[x\mid A,Z]\mid Z] = E[x\mid Z]$$
I try to ...
- 125
1
vote
1
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Does $E(X \mid Y,Z)=0$ imply $E(X \mid Y)=0$?
Does $E(X \mid Y,Z)=0$ imply $E(X \mid Y)=0$?
In other words, if we have $E(X \mid Y,Z)=0$ then can we also say $E(X \mid Y)=0$?
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