Law of Large Numbers and Central Limit Theorem

Where the earlier chapters described a single random variable, this one raises the viewpoint: what do very large amounts of data tend to do? Chebyshev’s inequality supplies the most basic guarantee — how far a variable may stray from its mean is bounded. The law of large numbers then shows that sample averages settle onto the true mean, and the central limit theorem reveals that the sample average is itself approximately normal. Most of the interval-estimation and hypothesis-testing formulas in practice trace back to that last theorem.