How is $E_q[\log p(x,z)] - E_q[\log q(z|x)]$ equal to$ E_{q(z|x)}[\log p(x|z)] - KL(q(z|x) || p(z))$?
48492
KL divergence of q(z|x) || p(z|x)
25618
$x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
72735
Understanding the proof of a formula for $p^e\Vert n!$
3273
Trouble in proving that $\|x\|_p = \max|x_j|$
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
122603
How does $\mathcal E(\rho)=\mathrm{Tr}_{env}[U(\rho\otimes\rho_{env})U^\dagger]$ turn into $P_0\rho P_0+P_1\rho P_1$?
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] $
100801
A $\log \Gamma $ identity: Where does it come from?
147705
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
35277
Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
107058
Prove that $E(X\ln X)\le E X E\ln X$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely