Central Limit Theorem: New SOCR Applet and Demonstration Activity.

Law of Large Numbers: the Theory, Applications and Technology-based Education.

Modern approaches for technology-based blended education utilize a variety of recently developed novel pedagogical, computational and network resources. Such attempts employ technology to deliver integrated, dynamically-linked, interactive-content and heterogeneous learning environments, which may improve student comprehension and information retention. In this paper, we describe one such innov...

Confidence Interval Based Parameter Estimation—A New SOCR Applet and Activity

Many scientific investigations depend on obtaining data-driven, accurate, robust and computationally-tractable parameter estimates. In the face of unavoidable intrinsic variability, there are different algorithmic approaches, prior assumptions and fundamental principles for computing point and interval estimates. Efficient and reliable parameter estimation is critical in making inference about ...

SOCR Motion Charts: An Efficient, Open-Source, Interactive and Dynamic Applet for Visualizing Longitudinal Multivariate Data.

The amount, complexity and provenance of data have dramatically increased in the past five years. Visualization of observed and simulated data is a critical component of any social, environmental, biomedical or scientific quest. Dynamic, exploratory and interactive visualization of multivariate data, without preprocessing by dimensionality reduction, remains a nearly insurmountable challenge. T...

Central and Local Limit Theories in Markov Dependent Random Variables

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...