Central Limit Theorem
(1.4 hours to learn)
The Central Limit Theorem states that the sum of a large number of independent, identically distributed random variables is approximately Gaussian. It can be used to approximate the probability that a sum of independent random variables lies within some range, even if the distributions are otherwise hard to work with. This theorem is one of the reasons that Gaussian distributions are so ubiquitous in statistics and probabilistic modeling.
This concept has the prerequisites:
- Know the statement of the central limit theorem
- Be able to use it to estimate the distribution of a sum of i.i.d. random variables
- Prove the theorem
Core resources (read/watch one of the following)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 5.7, "The Central Limit Theorem," pages 282-290
→ A First Course in Probability
An introductory probability textbook.
Location: Section 8.3, "The Central Limit Theorem," pages 434-443
Supplemental resources (the following are optional, but you may find them useful)
→ Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
→ Stats.Stackexchange Question: What intuitive explanation is there for the central limit theorem?
Location: answer from user 'whuber'
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 5.3, "Convergence in distribution and the Central Limit Theorem," pages 181-188
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation