If $X$ and $Y$ are identically distributed, not necessarily independent, show that $cov(X+Y,X-Y)=0$
120957
show that Cov(X+ Y, X-Y)= Var(X) - Var(Y)
156092
Existence of independent and identically distributed random variables.
62053
If $X$ and $Y$ are independent Normal variables each with mean zero, then $\frac{XY}{\sqrt{X^2+Y^2}}$ is also a Normal variable
142818
X,Y are independent standard normal distributed then what is the distribution of $\frac{X}{X+Y}$
92054
$X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$
150141
Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
135085
The mutual density of $X,Y$ in $\{|t|+|s|<1\}$ is constant, are $X,Y$ independent?
122929
Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
85790
Product of two random variables that has exponential distribution
23603
Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
45143
Identify $E(X\mid X+Y)$ for $X$ and $Y$ independent and Poisson
92917
If two Gaussian random variables are uncorrelated, they are statistically independent
133833
If $E(Y\mid X)$ is constant then $X, Y$ are uncorrelated.
136707
Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
116975
Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
14079
On the proof that every positive continuous random variable with the memoryless property is exponentially distributed