Archive for March, 2016

Coin flip

Indeed, but what is the distribution of the sample variance?

Yes, non-trivial functions of random variables can be constant functions. So you should be a bit more careful when you write such functions of rv’s down, because they may not thankfully fluctuate and they won’t give you all the nice results that randomness has to offer.

One example very close to home and to introductory statistics, is the asymptotic distribution of the sample variance, coming from a sample of i.i.d Dichotomous Uniform random variables. The most well known representative of this class of random variables, in fact a super-star, is the Bernoulli distribution with probability parameter p=0.5: a fair coin, in other words.

What happens is that for such variables, the asymptotic distribution of the sample variance is not normal. Find out why by downloading the following short Technical Report I have written some months ago, when I hit upon the matter.

Asympt distr of sample variance dichotomous rv’s Technical Report