15. Video: Two Useful Theorems - Law of Large Numbers

Two important mathematical theorems for working with sampling distributions include:

1. Law of Large Numbers
2. Central Limit Theorem

The Law of Large Numbers says that as our sample size increases, the sample mean gets closer to the population mean, but how did we determine that the sample mean would estimate a population mean in the first place? How would we identify another relationship between parameter and statistic like this in the future?

Three of the most common ways are with the following estimation techniques:

• Maximum Likelihood Estimation

• [Method of Moments Estimation][https://en.wikipedia.org/wiki/Method_of_moments]

• Bayesian Estimation

Though these are beyond the scope of what is covered in this course, these are techniques that should be well understood for Data Scientist's that may need to understand how to estimate some value that isn't as common as a mean or variance. Using one of these methods to determine a "best estimate", would be a necessity.