Independence of $x = z_1^2 + z_2^2$ and $y = z_2 / z_1$, with $z_1, z_2$ having a standart normal distribution
118867
Independence of Gaussian variables
145294
Independence of linear combination of multivariate distribution
24336
How can I obtain a Cauchy distribution from two standard normal distributions?
60063
Independence between random vectors
10482
Prove $(\sum_{i=1}^{n}X_{i},\sum_{i=1}^{n}X_{i}^{2})$ is not a complete statistic for $N(\mu,\mu^2)$ distribution
155900
Distribution of X+Y of a bivariate normally distributed (X,Y)
136707
Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
108005
A normal divided by $\sqrt{\chi^2(s)/s}$
1119
A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution -- proof
26717
Distribution of the difference of two normal random variables.
151302
If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
148932
Question about correlations and independence
822
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
135641
Algebraic independence of exponentials
74570
Finding distribution of $\frac{X_1+X_2 X_3}{\sqrt{1+X_3^2}}$
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
49896
A criterion for independence based on Characteristic function