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Explore tail bounds in this 81-minute lecture from MIT's Principles of Discrete Applied Mathematics course, where you'll learn to bound the probability that a random variable deviates significantly from its mean. Master Markov's bound and Chebyshev's bound as fundamental tools for probability analysis, then apply Chebyshev's bound to prove the weak law of large numbers, a cornerstone theorem in probability theory that describes the convergence of sample averages to expected values.