Theory Overview

The Weak Law of Large Numbers (WLLN) is a fundamental theorem in probability. It states that for a set of independent and identically distributed (i.i.d.) random variables, the sample mean will converge **in probability** to the true theoretical mean (or expected value) as the number of samples increases.

\( \bar{X}_n = \frac{1}{n}\sum_{i=1}^n X_i \xrightarrow{P} \mu \text{ as } n \to \infty \)

Procedure

• Select a probability distribution (e.g., Bernoulli, Normal) from the dropdown menu.
• Adjust the parameters for your chosen distribution. The theoretical mean will update automatically.
• Set the maximum number of samples (n) to generate using the slider.
• Click **"Run Experiment"**.
• Watch the plot and the observations panel update in real-time for 5 seconds. The y-axis of the plot is fixed to provide a stable frame of reference for the convergence.