Is it required to prove that random variables $X$ and $Y$ are not independent?
48270
How to prove that the random variables $X$ and $X^2$ are not independent?
86729
Are squares of independent random variables independent?
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
68137
Independence and conditional independence between random variables
57451
Independent variable = Random variable?
151302
If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
127052
Independence of non-constant real variables
150141
Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
10482
Prove $(\sum_{i=1}^{n}X_{i},\sum_{i=1}^{n}X_{i}^{2})$ is not a complete statistic for $N(\mu,\mu^2)$ distribution
136707
Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
127903
Why can 2 uncorrelated random variables be dependent?
126963
Is the sum of two variables independent of a third variable, if they are so on their own?
153393
Is there a *simple* example showing that uncorrelated random variables need not be independent?
113255
$X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
82279
Prove that it is a random variable iff it is constant on each partition
62007
Durrett Example 1.9 - Pairwise independence does not imply mutual independence?