Let $X \sim exp(\lambda)$ be independent of $Y \sim exp(\lambda)$ compute $E[X|X+Y]$
105850
Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions
102399
Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $
116975
Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
1264
Find the probability of an event determined by an inequality on exponential random variables
113255
$X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
129584
How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
151996
Calculate the expected value of $Y=e^X$ where $X \sim N(\mu, \sigma^2)$
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
62605
How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
124827
Show that $Y\sim N(a+A\mu,AVA^T)$
71794
Compute the mean of $(1 + X)^{-1}$ where $X$ is Poisson$(\lambda)$
74054
Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
32407
Prove $\exp(x+y) = \exp(x) \exp(y)$ for $\exp(x) = \sum_{n=0}^\infty \frac {x^n}{n!}$
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
9005
How to calculate the conditional mean of $E(X\mid X<Y)$?
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$