Key Properties and Central Theorems in Probability and Statistics - Corroborated by Simulations and Animations

Probability and the methods of statistical inference are highlighted by theoretical concepts, which are far from intuitive conceptions. A more direct approach beyond the mathematical exposition of the theorems is a basic requirement of educational statistics not only for students of studies different from mathematics. Also, the focus within mathematics lies heavily on the derivation of the mathematical connections and their logical proof relative to axioms and optimizing criteria. For example, the central limit theorem is hardly open to a full proof even to mathematics students. And in the proof, the used concepts - the characteristics function eg. - precludes understanding of the most relevant parts. It is not only the convergence of the distribution of the standardized statistics under scrutiny to the standard normal distribution. The central limit theorem incorporates also the speed of convergence to the limiting distribution, which is highly influenced by the shape of the distribution of a single random variable. To clarify such issues enhances the central limit theorem and the resulting importance of the normal distribution (even for non-parametric statistics). In the lecture, a spreadsheet will be used to implement the simulations and animations.