Contents

• Strong Law of Large Numbers
• Monte Carlo Simulation with Poisson Distribution
• Monte Carlo Simulation with Bernoulli Distribution
• Interactive

Strong Law of Large Numbers

• Let X₁, X₂, …X_n be an infinite sequence of independent random variables with the same probability distribution and the same mean µ.  Then:
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• For example, let  X₁, X₂, …X_n 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

Interactive

View Law of Large Numbers Interactive

Mathematica Demonstration by Paul Savory