Is it true that $X$ and $Y$ gaussian and $\mathbb E[XY]=0\implies X$ and $Y$ independent?
92917
If two Gaussian random variables are uncorrelated, they are statistically independent
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
16948
Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
54461
Showing independence of random variables
59577
Simple examples of uncorrelated but not independent $X$ and $Y$
88676
Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability
135085
The mutual density of $X,Y$ in $\{|t|+|s|<1\}$ is constant, are $X,Y$ independent?
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
30824
Pairwise independence of Random variables does not imply indendence
113526
Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?
122719
Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$
131026
Covariance and independence?
29339
Are functions of independent variables also independent?
46865
Proof of linearity for expectation given random variables are dependent
33907
The product of a normal and Rademacher variables, independent from each other
149362
Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
35454
Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?