If $X_{1}, X_{2}$ is a r.s. from $N(0,\sigma^2)$ (Scale Family) show that $\frac{X_1}{X_2}\sim \operatorname{Cauchy}(0,1)$
58338
How calculate the probability density function of $Z = X_1/X_2$
90055
Show that $\mathcal P(x)\notin x$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
45220
Proving the sum of two independent Cauchy Random Variables is Cauchy
131626
Finding the distribution of $\|X-\mu \|_\Sigma^2$ with $X \sim N(\mu,\Sigma)$
154945
$|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
122929
Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
86535
Prove quotient of two $N(0,1)$ is $\text{Cauchy}(0,1)$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy
54427
$\left|x_{n+1} - x_n\right| < C\left|x_n - x_{n-1}\right|$ prove this is Cauchy
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
14168
Prove the following sequence is a Cauchy Sequence
54982
How to prove that $x_n=1+\frac{1}{2!}+\cdots+\frac{1}{n!}$ is a Cauchy sequence?
37283
Show that $\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment functions