Does $\varphi_{X+Y}(t)=\varphi_X(t)\varphi_Y(t)$ imply independence of $X$ and $Y$?
39378
Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.
54461
Showing independence of random variables
114309
T-invariant linear independence
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
73367
On $E[E[Y|X]|X]= E[Y|X]$
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
122719
Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
12083
How to prove $\limsup (x_{n}+y_{n})=\lim x_{n}+\limsup y_{n}$?
71016
\varepsilon vs. \epsilon
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
135085
The mutual density of $X,Y$ in $\{|t|+|s|<1\}$ is constant, are $X,Y$ independent?
128639
Homoskedasticity Assumption: Var(y|x)=Var(u|x)=constant?
157920
Can I define $y=y(x)$?
66391
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
20581
How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
20750
Proving an equality regarding fully independent events