How can we explain the fact that $\mathbb E\left( {\mathbb E\left( {X|Y} \right)} \right) = \mathbb E(X)$?
57170
Intuitive explanation of the tower property of conditional expectation
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
129170
Deriving the expectation of $[\hat X,\hat H]$
83183
Why is $\langle x| x' \rangle=\delta(x-x')$?
5350
Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
99165
How to prove that for Brownian motion in $(a, b)$ $\mathbb{E}^x[\min(H_a, H_b)] = (x-a)(b-x)$?
134696
How can I show that the conditional expectation $E(X\mid X)=X$?
150321
How do you prove Cov $\left( \bar{X} , X_i - \bar{X} \right) = 0$?
130765
Linear dependence of $\left\{x^{n}\,\colon\, n\in\mathbb{N}\right\}$
130854
Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$
66991
One confusion over conditional expectation
18839
Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
33054
Given a joint density function, what is the conditional expectation $E[Y|x]$?
69715
Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely