An Example: The Law of Large Numbers

 
[From Wikipedia: http://en.wikipedia.org/wiki/Law_of_large_numbers]
 
 
 
The illustration above demonstrates the law of large numbers using a particular run of rolls of a single die. As the number of rolls in this run increases, the average of the values of all the results approaches 3.5 [the average value of all faces: (1 + 2 + 3 + 4 + 5 + 6)/6]. Though early on in the run (at left) the mean value may fluctuate wildly, over a large number of rolls (at right) the mean value will move closer and closer to the expected (theoretical) value of 3.5.  
 


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