CHAPTER 25The Limits of (Statistical) Independence

Everything we know is based on observable phenomena subject to chance variation. This is how probability works: Observe some data, assign some distributions, and derive rules that govern the behavior of chance. The workhorse idea that makes this more than arbitrary guessing is the limit-theorem notion. Limit theorems highlight how given observed frequencies converge to probability distributions that embody clearly defined rules for prediction.

The convergence imposes a useful regularity when the number of possible outcomes is fixed and bounded measureable sets are the framework. Namely, given an independent sequence of random variables with finite mean and variance, as the sample size tends to ...

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