If $\frac{X+Y}{\sqrt{2}}\stackrel{d}{=}X\stackrel{d}{=}Y$, use the CLT to show that $X,Y\in N(0,1)$
4058
Suppose X and Y are i.i.d and $\frac{X+Y}{\sqrt{2}}\overset{d}=X\overset{d}=Y$, show that X has a normal distribution.
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
27068
Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
117320
Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
1932
How to show this equality of $\rho(X,Y)$
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.
151111
How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
108704
Help with proof of $|x+y| \geq |x|-|y|$
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $