Law of Large Numbers

Strong Law of Large Numbers
  • Let X1, X2, …Xn be an infinite sequence of independent random variables with the same probability distribution and the same mean µ.  Then:
  • For example, let  X1, X2, …Xn be random variables with the Poisson Distribution with mean 5.  Then the following statement has probability = 1:
    • As the number of random variables increases, their average approaches 5 (in the sense of mathematical limit).
  • View Random Variables and Probability Distributions
Monte Carlo Simulation
With Poisson Distribution with Mean 5
Monte Carlo Simulation
With Bernoulli Distribution with Probability = 0.6

View Law of Large Numbers Interactive

Mathematica Demonstration by Paul Savory