If $X$ and $Y$ are both independent from $\mathscr {F}$, is $f(X,Y)$ also independent from $\mathscr{F}$?
39409
$X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$
86729
Are squares of independent random variables independent?
7665
If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
47810
$C(X)$ is separable when $X$ is compact?
148932
Question about correlations and independence
142855
If $A$, $B$ are both pairwise independent of $C$, do we have that $A \cap B$ is also independent of $C$?
3040
Independence of points from same underlying function
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
142873
What does the function f: x ↦ y mean?
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
37892
If $X$ is homeomorphic to $Y$ then is $X/{\sim}$ homeomorphic to $Y/{\sim'}$?/
81488
If a continuous function$f: (X, \mathscr T_X) \to (Y, \mathscr T_Y)$ is injective (Given $Y$ is Hausdorff), show that X is hausdorff
65827
When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
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.