if X and Y are Gaussian and independent and w=Inf P(X+Y |-w<=X-Y<=w) is
equal to the unconditional probability P(X+Y). This implies that Z=X+Y
follows a Gaussian with mean E(X)+E(Y) and Var(Z)=Var(X)+Var(Y).
If w is smaller than Inf:
Intuition suggests that Var(Z) > Var(X)+Var(Y) but does anyone know a
formula / approximation for this?
And is there a approximation for the case that X and Y are dependent.
Second issue:
Can the resulting distribution of Z approximated by a Gaussian distribution?
P(X+Y |-w<=X-Y<=w) ... if X and Y are Gaussian and independent and w=Inf then P(X+Y ... And is there a approximation for the case that X and Y are dependent. ... Can the resulting distribution of Z approximated by a Gaussian distribution?... (sci.stat.edu)
Re: P(X+Y |-w<=X-Y<=w) ... if X and Y are Gaussian and independent and w=Inf then P(X+Y ... And is there a approximation for the case that X and Y are dependent. ... I would appreciate any good reference to textbooks or articles. ... Can the resulting distribution of Z approximated by a Gaussian distribution?... (sci.stat.edu)
Re: FFT test with few kbits ... ]>>> average to N/2 while the rest should average to zero.... ]>>> able to test that they have the same gaussian distribution as the ... ]> output of the DFT is a weighted sum of N random inputs. ... ]> Gaussian distributed.... (sci.crypt)
Re: Add Noise ... >But by the central limit theorem, it approaches Gaussian as N ... >approaches infinity. ... The variance of the common uniform is 1/12 so the sum of 12 of them ... It is a workable approximation at 1:00 ... (comp.lang.fortran)
Re: random points with a given dsitribution in rectangle ...Gaussian variates will not necessarily fit in a rectangle. ...bivariate Gaussian distribution can be obtained by using ...Gaussian distribution can be obtained by using mvnrnd from the statistics ... If you dont have that toolbox then there are some simple tricks ... (comp.soft-sys.matlab)
