Test for randomness

Pls excuse my naive questioning.

If you have a set of measurements for a random variable X and you take
the mean and standard deviation is the ratio (mean/std. dev) a
measure of randomness? If not, what is it?

 

It is the inverse of the "coefficient of variation"
http://en.wikipedia.org/wiki/Coefficient_of_variation
and probably only meaningful for positive random variables

 

It's an "effect size", the standardized distance of the mean from 0,
a quick and dirty measure of the extent to which the distribution
overlaps 0.

 

With Maurice Allais' discovery of his Theorem T (c. 1985) there can be no
definitive test for randomness.

 

I cannot find this theorem anywhere.

An example of my problem: I trade stocks and I sometines win and
sometimes lose. I call the value Ti. Given a large i, > 1000, is there
any way to determines whether these values are random or there is a
certain strategy behind them? In other words, is there a way to test
if the Ti's could have been obtained by chance?

 

Allais wrote a contribution to a collection of articles on causality.
Unfortunately I do not have the reference info: Arts Library @ University
of Waterloo.

Given a particular model and probability distribution one may be able to
test different hypotheses. But whatever hypotheses you wish to test you
should consider that there is a maximum that you can lose on any stock and
that stock prices may not be independent of one another.