Unit sphere contains a line segment $[x,y]$, prove x and y are linearly independent.
127248
Norm and unit sphere
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
33526
How to prove this beautiful statement on linear forms using induction?
63614
Showing a Normal and a Chi square are independent
150141
Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
146664
The union of two linearly independent subsets
91087
For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
143732
Prove random variable $Y_0$ and $\sigma$-algebra $\mathscr{R}$ are independent.
25618
$x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
66298
Prove that $\alpha(t)$ lies on a sphere.
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
90970
How to prove the line exist?
16582
Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions