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Probability and Measure, Lecture 11: The Strong Law of Large Numbers
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We prove the weak and strong laws of large numbers. The main tools we need to achieve this are Chebyshev's inequality and the Borel-Cantelli lemmas. Note how the strong law requires a lot more work than the weak law to prove. At the end, we simulate in RStudio to visually see what happens as a normalized summation converges.