Is $X^2-Y^2/ \sqrt{X^2+Y^2}$ normal where $X,Y\sim N(0,1)$
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 $N(0,\frac{1}{4})$
30431
How is the notation $X\sim N(\mu,\sigma^2)$ read?
137983
Normalisation of $k[x,y]/(y^2-x^2(x-1))$
131626
Finding the distribution of $\|X-\mu \|_\Sigma^2$ with $X \sim N(\mu,\Sigma)$
69172
$y'=$ ${-x+\sqrt{(x^2+4y)}}\over 2$ , $y(2)=-1$
43506
Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$
158447
Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
141438
If $X$ is distributed $\mathcal{N}\sim(\mu,1)$ then what is the PDF of $X^2$?
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
144042
On the functional square root of $x^2+1$
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
65784
If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$
103618
Calculate $E(X^{2n})$ where $X$ is normal (0,1)
84074
3 normals on a parabola
101754
Transformation of Random Variable $Y = X^2$
3390
finding the real values of $x$ such that : $x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$
22129
Why is $\sqrt{\sum_{i=1}^n |v_i|^2} \leq \sum_{i=1}^n |v_i|$ true?