The Central Limit Theorem

This app provides an interactive platform for exploring the behavior of sample averages across four different statistical distributions: continuous uniform, binomial, exponential, and Cauchy. Users can adjust key parameters of each distribution and observe through real-time histograms how sample averages converge towards a normal distribution, demonstrating the Central Limit Theorem.

The Central Limit Theorem

Select a distribution and start sampling to observe how the shape of the sample histogram evolves as the sample size increases.

Probability distribution:

Uniform

\( \ [a, b] = \ \)

[0.00, 1.00]

Binomial

\(p = \ \)

0.50

Exponential

\( \lambda = \ \)

1.00

Cauchy

\( \alpha = \ \)

1.50

Select a distribution and start sampling to observe how the shape of the sample histogram evolves as the sample size increases.

Normalized sample average frequency histogram

Samples per second: 1.0