Central Limit Theorem for Dependent Variables

The Central Limit Theorem (CLT) generally applies to independent random variables, stating that the average of a large number of samples will approximate a normal distribution, regardless of the original data's distribution. For dependent variables, the situation is more complex. When variables influence each other, their relationships can affect the distribution of averages. In such cases, the CLT may still hold under specific conditions, but the convergence to a normal distribution can be slower or require larger samples. Understanding these nuances helps in accurately applying statistical methods in real-world scenarios where variables are often interconnected.