7.1.0 Limit Theorems
In this section, we will discuss two important theorems in probability, the law of large numbers (LLN) and the central limit theorem (CLT). The LLN basically states that the average of a large number of i.i.d. random variables converges to the expected value. The CLT states that, under some conditions, the sum of a large number of random variables has an approximately normal distribution.