If $(X,Y)$ are i.i.d. exponential then $X/(X+Y)$ follows a Beta distribution
26860
X,Y are independent exponentially distributed then what is the distribution of X/(X+Y)
26833
Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
100916
Finding $\mathrm{Cov}(X,Y)$ and $E(X\mid Y=y)$ given the joint density of $(X,Y)$
85818
$E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
73189
Proving Bernoulli is the limit of Beta
143701
About logistic distribution and showing $Y=\frac{1}{1+e^{-X}}$ has an uniform distribution over (0,1)
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
37474
Why is the sample distribution the Exponential distribution Gamma distributed?
40078
Calculate $E(Y)$ and $Var(Y)$ given the random variable which is exponentially distributed
43500
How to show this curious combination of Exponential order statistics has a Chi-squared distribution?
39897
Mean and variance of a Beta distribution with $\alpha \ge 1$ or $\beta \ge 1$?
81077
Prove that $E(X^n)^{1/n}$ is non-decreasing for non-negative random variables
65784
If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$
33332
A classic exponential inequality: $x^y+y^x>1$
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
112845
Show that the Beta Function $\beta (x,y)$ Converges When $x \gt 0, \space y \gt 0$
1909
Consistency of an order statistic in exponential distribution