What's the difference between probability and statistics?
Today I just came back from a student seminar in our department. And I heard that for the Pareto distribution, it is kind of difficult to estimate the parameter. There are hundreds of estimations of the parameter and they differ a lot, which means there is no way to estimate it. Thus, I am just wondering what is statistics? Statistics could not estimate such a parameter? Statistics relies what to get the estimation? Not Probability properties of this distribution? Statistics just relies on a mass data set and how could it come up a statistic to estimate the parameter of interest? We use mean to estimate the expectation just because of the central limit theorem, which is totally probability. So what is statistics?