Suppose $\mathbf{X, Y}$ are independent random vectors. Are their components independent?
31133
Functions of Independent Random Variables
16673
If $X$ and $Y$ are independent then $f(X)$ and $g(Y)$ are also independent.
57451
Independent variable = Random variable?
100873
Let $\mathbf{Y}$ be a random vector. Are $k$th moments of $\mathbf{Y}$ considered?
127052
Independence of non-constant real variables
88431
Jointly Gaussian uncorrelated random variables are independent
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
101627
Variance of product of 2 independent random vector
103780
Independence of disjoint events
147866
If X,Y and Z are independent, are X and YZ independent?
30500
Independence of ratios of independent variates
126963
Is the sum of two variables independent of a third variable, if they are so on their own?
19244
Covariance of a random vector after a linear transformation
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
113255
$X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
95928
Independence and orthogonality
49463
Probability : Venn diagrams; independent