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seen Oct 30 '10 at 21:52

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