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 Aug 25 comment What is known about the Gaussian measure of the unit ball in a Hilbert Space? Or, the site : books.google.fr/… Aug 25 comment What is known about the Gaussian measure of the unit ball in a Hilbert Space? For more detail, you can see the book of Michel Ledoux - "The Concentration of Measure Phenomenon. Aug 25 answered What is known about the Gaussian measure of the unit ball in a Hilbert Space? Aug 24 answered The density of x_1^n+x_2^n where x_i are Gaussian Aug 22 awarded Teacher Aug 22 answered Kernel width in Kernel density estimation Aug 21 answered connection between the Gaussian and the Cauchy distribution Aug 21 comment connection between the Gaussian and the Cauchy distribution Jon Peterson, you are correct. But why does it directly the calcul of cdf and pdf of $Y/X$, ie \begin{eqnarray*} F_Z(z)&=&\mathbb P(Z\leq z)=\mathbb P(Y/X\leq z)=\mathbb P(Y\leq zX)\\ &=&\mathbb P(Y\leq zX,\,X> 0)+ \mathbb P(Y\geq zX,\,X< 0),\,\, \mbox{that implies}\\ f_Z(z)&=& \frac{dF_Z(z)}{dz}=\int_{-\infty}^{+\infty}|x|f_Y(zx)f_X(x)\, dx\\ &=&\frac{1}{2\pi}\int_{-\infty}^{+\infty}|x|e^{-(z^2+1)x^2/2}\, dx=\frac{1}{\pi(x^2+1)}. \end{eqnarray*} The difficulty I encountered is how to prove that the characteristic function of the variable $Y / X$ is the same as the Cauchy distribution ? Aug 21 answered Estimating the mean of a truncated gaussian curve