if $X\sim\exp\left(1\right)$ and $Y\sim\exp\left(1\right)$ independent, find $f_{X|Z}(x|z)$ where $Z=X+Y$
94636
Conditional distribution of exponential random variable conditioned on sum of i.i.d. exponential random variables
43703
Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
113255
$X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
147159
Determine the set of values of $\exp(1/z)$ for $0<|z|<r$
46844
Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
82729
Prove that $\mathrm E\left({\max}\left\{X^2 , Y^2\right\} \right) \leq 1 + \sqrt{1 - \rho^2}$ where $\rho$ is their correlation.
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
105850
Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions
73367
On $E[E[Y|X]|X]= E[Y|X]$
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
64844
Finding $E(|X_1|\ |\max |X_i| )$
76884
Are $X$ and $X+Y$ independent, if $X$ and $Y$ are independent?
143765
To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$