Timeline for Independence of r.v.'s following a distribution that is the ratio between complex Gaussian and Chi-square r.v.'s

9 events

when toggle format	what		by	license	comment
Feb 7, 2019 at 9:11	vote	accept	Felipe Augusto de Figueiredo
Feb 7, 2019 at 7:18	comment	added	Carlo Beenakker		${\cal O}(M^{-7})$ means that the next order term in an expansion in powers of $1/M$ is of order $M^{-7}$; I used Mathematica for the integrals; it will not return an answer for a symbolic $M$, but it will for any integer $M$ and then the polynomial in the denominator is easily obtained; perhaps there is a way to obtain this directly, but to demonstrate the absence of independence of $z_1$ and $z_2$ this suffices.
Feb 6, 2019 at 22:48	comment	added	Felipe Augusto de Figueiredo		One more question, how did you find $a^2\,\mathbb{E}[\|z_1\|^2\|z_2\|^2]=\frac{1}{4M(M+1)(M-1)(M-2)}$?
Feb 6, 2019 at 22:43	comment	added	Felipe Augusto de Figueiredo		What do you mean by ${\cal O}(M^{-7})$?
Feb 6, 2019 at 16:38	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 22 characters in body
Feb 6, 2019 at 15:14	history	edited	Carlo Beenakker	CC BY-SA 4.0	deleted 6 characters in body
Feb 6, 2019 at 15:09	history	edited	Carlo Beenakker	CC BY-SA 4.0	deleted 295 characters in body
Feb 6, 2019 at 15:03	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 282 characters in body
Feb 6, 2019 at 12:42	history	answered	Carlo Beenakker	CC BY-SA 4.0