The First Moment Principle states that a random variable X is at most E(X) with positive probability. Often we require that X is near E(X) with very high probability. When this is the case, we say that X is concentrated. In this book, we will see a number of tools for proving that a random variable is concentrated, including Talagrand’s Inequality and Azuma’s Inequality. In this chapter, we begin with the simplest such tool, the Chernoff Bound.
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