Law of Large Numbers Simulator

As the number of trials grows, the sample mean converges to the theoretical mean E[X]. Explore how fast convergence happens across different distributions.

Press Play or Step to begin

Active Model

BERNOULLI (p=0.50)

Running Average (Cumulative Sample Mean)

±1 SE band

As the number of trials increases, the sample mean gets closer to the theoretical mean — this is the Law of Large Numbers.

Observed Outcome Frequencies