# Intuition Behind the Law of Large Numbers and Central Limit Theorem

## Primary Notion and Applications in Probability Estimation

I wouldn’t be going out on a limb to say the central limit theorem (CLT) is the most astonishing result bridging the gap between probability and statistics. Herein I discuss the primary notion and major applications.

This article is broken up into the following sections.

**Law of Large Numbers****Central Limit Theorem****Framing for Applications****Shameless Plug for****Quant Guild**

## Law of Large Numbers (LLN)

If you wish to disregard the math the LLM primarily defines the stability and reliability of large sample averages.

If you wish to understand what I mean by *stability* and *reliability*, I will formally define the LLN. With finite mean and variance, for any positive epsilon, it follows…

As the sample size increases indefinitely the difference between the estimate given by a sample and the population parameter will be bound by any arbitrary distance with certainty.

In other words, as the sample gets closer to the population the distance between the estimate and the true population…