Show $\operatorname{Var}(X)=E(\operatorname{Var}(X\vert \mathcal{F}))+\operatorname{Var}(E(X\vert \mathcal{F}))$
139722
Computing the expectation of conditional variance in 2 ways
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
25652
Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
132392
Properties of Expectation
80803
Conditional expectation $E[\log(1+X) \mid X>t]$
143765
To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
101687
$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $
36417
Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?
101499
Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes
2635
equality of two operators...
103053
give a variable to an operator
68116
How to derive this version of variance formula
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
13561
Show: $E(|X|)\leqslant\liminf_{n\to\infty} E(|X_n|)$