This post in the Wolfram Blog describes work in progress enhance Mathematica 9's probability & statistics and to adding new knowledge to Wolfram|Alpha on a daily base.
It is amazing how fast Mathematica's knowledge base of special functions grew from the very beginning and how fast the knowledge of probability distributions grew from Mathematica 7 to 9 and that a growing number of properties ca be calculated. To calculate them will need to generate functions that are expressed by named mathematical functions - so everything is linked ....
But Wolfram|Alpha will go beyond. It wants to answer quantitative questions of any form - and consequently, thus includes probability distributions. And it is a goal to haven them completed and calculate a vast variety of properties.
To incorporate the complete list of probability distributions and properties into Wolfram|Alpha will happen in the near future. They will be represented for manipulation in an interactive Mathematica document called "The Ultimate Univariate Probability Distribution Explorer", proving again how powerful Mathematica's document centered architecture in combination with its dynamic visualization is.
I again think of econometrics applications and econophysics approaches for better insight in, say quantitative finance and much more .....
