If $X$ and $Y$ are independent. How about $X^2$ and $Y$? And how about $f(X)$ and $g(Y)$?
86729
Are squares of independent random variables independent?
131026
Covariance and independence?
29339
Are functions of independent variables also independent?
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
136707
Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
5595
$x^y = y^x$ for integers $x$ and $y$
142855
If $A$, $B$ are both pairwise independent of $C$, do we have that $A \cap B$ is also independent of $C$?
116975
Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
79457
Geometric random variables $X_1:G(p_1)$ $X_2:G(p_2)$ $X_3:G(p_3)$ are independent, prove the following :
77133
$g'(x) = \frac{1}{x}$ for all $x > 0$ and $g(1) = 0$. Prove that $g(xy) = g(x) + g(y)$ for all $x, y > 0$.
126963
Is the sum of two variables independent of a third variable, if they are so on their own?
127052
Independence of non-constant real variables
147866
If X,Y and Z are independent, are X and YZ independent?