Let Z be a standard normal R.V.. Show that Sgn(Z) and $\lvert Z\rvert$ are independent.
57055
Are $|X|$ and $\operatorname{sgn}(X)$ independent?
64314
Proof of certain Gaussian integral form
12004
Intuitive reason why jointly normal and uncorrelated imply independence
71819
Prove that $H$ is normal.
110832
$F_\sigma$-subsets in a normal space can be separated
153448
Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
95928
Independence and orthogonality
135641
Algebraic independence of exponentials
108560
Proof of a Gaussian Integral property
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
78997
If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.
142325
Two independent geometric random variables - proof of sum
48811
Characteristic function of product of normal random variables
54461
Showing independence of random variables
45220
Proving the sum of two independent Cauchy Random Variables is Cauchy