$\overline{X}$ and $S^2$ are independent
9665
Proof of the independence of the sample mean and sample variance
30796
Is the set of irrationals separable as a subspace of the real line?
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?
86635
Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
623
variation of a function over countable intervals
57122
If $E$ is a connected space, then so is $\overline{E}$.
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
150141
Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
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 $N(0,\frac{1}{4})$
72044
prove $x \mapsto x^2$ is continuous
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
48270
How to prove that the random variables $X$ and $X^2$ are not independent?
3040
Independence of points from same underlying function
154572
Continuity of a function at an isolated point
63614
Showing a Normal and a Chi square are independent
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent