# 9: Central Limit Theorem

- Page ID
- 3162

- 9.1: Central Limit Theorem for Bernoulli Trials
- The second fundamental theorem of probability is the Central Limit Theorem.

- 9.2: Central Limit Theorem for Discrete Independent Trials
- We have illustrated the Central Limit Theorem in the case of Bernoulli trials, but this theorem applies to a much more general class of chance processes.

- 9.3: Central Limit Theorem for Continuous Independent Trials
- We have seen in Section 1.2 that the distribution function for the sum of a large number \(n\) of independent discrete random variables with mean \(\mu\) and variance \(\sigma^2\) tends to look like a normal density with mean \(n\mu\) and variance \(n\sigma^2\). Let us begin by looking at some examples to see whether such a result is even plausible.