3 ms·
"If I understand the CLT (big if) then the distribution of the _mean_ of a sample is, by the CLT, going to be Gaussian" Yes, for an infinite number of samples.
by lutorm 17y ago
"If I understand the CLT (big if) then the distribution of the _mean_ of a sample is, by the CLT, going to be Gaussian"
Yes, for an infinite number of samples. The rate at which is converges to a Gaussian, though, is strongly dependent on the distribution from which the measurements are drawn.
- joe_the_user 17y agoActually, not even this is not true! The Central Limit Theorem applies only to samples which have finite mean and variance (see: http://en.wikipedia.org/wiki/Central_limit_theorem http://en.wikipedia.org/wiki/Central_limit_theorem). Take a distribution which has infinite variance or mean and you can wind-up instead with one of the fractal distributions which Mandlebrot studied. see http://en.wikipedia.org/wiki/Stable_distribution http://en.wikipedia.org/wiki/Stable_distribution Distributions with infinite variance or mean are more common than one might imagine. Some might argue the stock market would qualify.
- lutorm 17y agoGood point. Distributions with infinite variance are less common in physics, so that's normally not something we have to worry about.