If $X$ and $Y$ are independent random variables, does it follow that $X^2$ and $Y$ are independent?
54461
Showing independence of random variables
33907
The product of a normal and Rademacher variables, independent from each other
26860
X,Y are independent exponentially distributed then what is the distribution of X/(X+Y)
84203
Let $X_1$ and $X_2$ are independent $N(0, \sigma^2)$ random variables. What is the distribution of $X_1^2 + X_2^2$?
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
127903
Why can 2 uncorrelated random variables be dependent?
61758
Limit question on independent random variables (Exercise 4.2.4 from Grimmett and Stirzaker)
38461
If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?
75842
Quotient Distribution of Positive Independent Random Variables
822
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
126988
Are two independent events $A$ and $B$ also conditionally independent given the event $C$?
127052
Independence of non-constant real variables
86729
Are squares of independent random variables independent?
9665
Proof of the independence of the sample mean and sample variance
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
62053
If $X$ and $Y$ are independent Normal variables each with mean zero, then $\frac{XY}{\sqrt{X^2+Y^2}}$ is also a Normal variable
154091
Is there any counterexample to show that $X,Y$ are two random variables and $E(X\mid Y)=E(X)$, but $X$ and $Y$ are not independent.