Limit Theorems
Limit Theorems are fundamental concepts in statistics and probability that describe the behavior of a sequence of random variables as the number of observations increases. The most well-known is the Central Limit Theorem, which states that, under certain conditions, the sum or average of a large number of independent random variables will approximate a normal distribution, regardless of the original distribution of the variables.
Another important limit theorem is the Law of Large Numbers, which asserts that as the number of trials increases, the sample average will converge to the expected value. These theorems are crucial for making inferences about populations based on sample data and are widely used in various fields, including economics, psychology, and engineering.