[Omnirizon]

for the statistically impaired:

binomial distribution simply means "number of successes over n trials"
so if there are 4 possible slots for a site, then there are four independent trials (one for each slot). Because they are independent, the probability for n slots is simply n times the probability of a success.

I think exponential is being used to describe the shape of a distribution where later trials are dependent on earlier trials, thus making the distribution drop off steeper. unlike the binomial distribution, there cannot be a test for 'slot 2' unless the test for 'slot 1' was successful. So obviously there will be fewer provinces with 2 or more sites.

To test these hypothesis, we would need to gather data on the number of sites that do appear in each province in the game, build the distribution they form, and compare it to a binomial and an exponential distribution, and see which one it more closely approximates. Comparing distributions like this is called a "Goodness of fit test", because we are seeing how well an observed distribution fits a hypothetical one.



strip out all the jargon and math-babble, and statistics (even math in general) is extremely simple. problem is, people have formed a myopic hyper-specialized language that, unfortunately, draws upon other words with other meanings in other contexts but completely different meanings when used in statistics. when one trys to ferret out meanings of words in statistics, they are faced with an impenetrable wall of formalized expressions which require prior explanation from someone familiar with the expressions and who can explain them in natural language along with noting the specialized, context specific, meanings of words. This problem has been compounded in the american school system by a systematic 'dumbing' of mathematics in american schools where math concepts are presented without explaining the underlying logic because it was believed it was 'too complex'. In reality, the underlying logic is very simple (thus why it is logical at all), and by leaving this out children are left feeling that they know 'a little bit about math' but that there is this whole mystical world behind this which takes hyper-specialized experts to understand. nothing is further from the truth, as evidinced by the way in which children in even underdeveloped countries with second-rate education systems outperform american children in mathematics.

ooops. I was ranting. sorry.