Procedure

Sub-experiment 1 : Different types of convergence

• Read the experiment setting. The random variable $X_n$ is defined there.
• Now enter a value of $\omega$ in the range $[0,1]$.
• Enter a block number $k$
• Observe how for any value of $\omega$ and any $k$, there will be a random variable $X_n$ in that block which has $X_n(\omega)=1$
• Additionally, also see that how the sequence ${X_n(\omega)}$ for $n=1,2,3...$ does not converge and does not have a limit.

Sub-experiment 2 : Weak Law of Large Numbers (Convergence in probability)

• Select a distribution type from the dropdown menu
• Adjust the parameters for your chosen distribution
• Set the maximum number of samples (n) using the slider and run the experiment.
• The red line shows the theoretical mean (µ) and the blue plot shows the sample mean.
• Watch how the sample mean converges to µ as n increases