Convergence in distribution is a concept in probability theory that describes how a sequence of random variables approaches a limiting distribution as the number of variables increases. Specifically, if the cumulative distribution functions (CDFs) of the random variables converge to a CDF of a limiting random variable, we say that the sequence converges in distribution. This type of convergence is often used in statistics and is essential for understanding the behavior of estimators. This concept is particularly important in the context of the Central Limit Theorem, which states that the sum of a large number of independent, identically distributed random variables will approximate a normal distribution, regardless of the original distribution. Convergence in distribution helps statisticians and researchers make inferences about populations based on sample data, facilitating the application of various statistical methods.