Law of Large Numbers (LLN) and Central Limit Theorem (CLT)
Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) are two fundamental concepts in probability and statistics that describe the behavior of large samples and their definition is:
Law of Large Numbers (LLN)
Law of Large Numbers states that as the number of trials or observations increases, the average of the results obtained will converge to the expected value.
Central Limit Theorem (CLT)
Central Limit Theorem states that the distribution of the sample mean of a sufficiently large number of independent, identically distributed (i.i.d.) random variables approaches a normal distribution, regardless of the original distribution of the variables.
- LLN focuses on the convergence of the sample mean to the population mean as the sample size grows.
- CLT focuses on the distribution of the sample mean, stating that it becomes approximately normal as the sample size grows.
Law of Large Numbers and the Central Limit Theorem are foundational principles in probability and statistics. LLN ensures that averages of large samples are reliable estimates of the population mean, while CLT justifies the use of the normal distribution for making inferences about sample means.
Law of Large Numbers
Law of Large Numbers (LLN) is a mathematical theorem that states the average of the results obtained from many independent random samples.
In this article, we have discussed the Law of Large Numbers definition, its limitations, examples and others in detail.
Table of Content
- What is Law of Large Numbers?
- Limitation of Law of Large Numbers
- Types of Law of Large Numbers
- Why is Law of Large Numbers Important?
- Law of Large Numbers (LLN) and Central Limit Theorem (CLT)
- Examples of Law of Large Numbers
- Law of Large Numbers in Finance