What is the Advantage of Using a Gaussian Distribution of Noise in a System?

[m~ray]

what is the advantage of using a gaussian distribution of noise (white/colored) in a system over any other distribution ??

 

[Nabeshin]

Do you mean other than the fact that this is what random noise actually looks like..?

 

[sophiecentaur]

Are you talking 'simulations'?

 

[m~ray]

okay so u mean to say all random number distributions naturally follow the gaussian distribution?? say we need to insert 10^10 numbers between 1-100, where all the 100 places are equally likely to be filled. so eben in this case u mean to say on an avg there will be more number of numbers in 51 and 50?? if yes, then why should it be like that, as all numbers are equally likely to be filled..

 

[Nabeshin]

No. Say you are picking numbers 1-100 completely at random, and you do this 10^10 times (This is the same as what you said, just phrased slightly differently). Now, the mean number of times you picked a given number will be 10^8 (10^10/100), but there will be some variation around this 10^8 mean and this variation will be described by a gaussian.

 

[sophiecentaur]

okay so u mean to say all random number distributions naturally follow the gaussian distribution?? say we need to insert 10^10 numbers between 1-100, where all the 100 places are equally likely to be filled. so eben in this case u mean to say on an avg there will be more number of numbers in 51 and 50?? if yes, then why should it be like that, as all numbers are equally likely to be filled..

You are misinterpreting what the Gaussian distribution means, I think. Each number is equally likely: no more 50s than 99s. But it is more likely that adding any random two together will give an answer nearer to 100 than to 200 or 2. So it's the average and not the individual number that counts.

 

[m~ray]

thanks a lot for the explanations. yes, the variation about the mean 10^8 describing a gaussian curve makes total sense now..

by the way, i am doing a project in stochastic resonance, and i want to learn more about stochastic processes, random numbers, probability theory, chaos and other related areas in the coming summer. Can u name me a few good books or other resources on such subjects?