A proof exercises of conditional expectation of sigma algebra
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
62317
Generating set of countable, co-countable sigma algebra on $\mathbb{R}$
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely
97870
Conditional expectation in AR(1) process
83830
Sigma algebra generated by the set of all singletons
94662
Tower property of conditional expectation
9762
Why do we need sigma-algebras to define probability spaces?
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
124261
Expectation of nonnegative RV
53642
Cardinality of Borel sigma algebra
10702
Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
111915
Almost Sure Convergence and Bounded Expectation
34278
A basic question on expectation of distribution composed random variables
74054
Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
144359
A random variable that induces a $\sigma$-algebra the same as the one in the sample space
29565
Conditional Expectation of Bernoulli R.V.
20750
Proving an equality regarding fully independent events