Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
43228
What is the intuition behind beta distribution?
151297
Second order partial of $f(x,y)=\frac{xy(x^2-y^2)}{x^2+y^2}$
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
65784
If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
155341
Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
143375
Showing that $\lim_{(x,y) \to (0, 0)}\frac{xy^2}{x^2+y^2} = 0$
109994
Show discontinuity of $\frac{xy}{x^2+y^2}$
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
38773
Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
7802
Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer