If X~N(0,1) and Y~N(0,1) then X+Y~N(0,2)
61101
Sum of two independent normal distributed random variables
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
25312
Let $(x_n)\downarrow 0$ and $\sum x_n\to s$. Then $(n\cdot x_n)\to 0$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
67214
Function $ y = x^n - nx$, where $x \geq 0$ and $n \geq 2$.
120736
If xy + yz + zx = 1, ...........
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
53443
Does $a_n \sim b_n$ imply $\sum_n a_n \sim \sum_n b_n$ for $a_n, b_n>0$?
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
93634
X,Y,Z independent and $\sim N(1,1)$. Find $P(X+Y \geqq 3Z)$