Convergence in distribution

Convergence in distribution describes how a sequence of random variables becomes increasingly similar to a specific probability distribution as the sample size grows. Essentially, as you observe more and more data points, the behavior of these variables stabilizes and resembles a particular pattern or distribution, like the bell curve. This concept is fundamental in statistics and probability, as it explains how complex random phenomena can be approximated by well-understood distributions when dealing with large samples. It doesn't require the variables themselves to get closer in value, just their overall distribution to match a target pattern more closely.