Intro to Probability
Asymptotic normality refers to the property of a sequence of random variables that, as the sample size increases, the distribution of the standardized sample mean approaches a normal distribution. This concept is fundamentally connected to the Central Limit Theorem, which asserts that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the shape of the population distribution, as long as the population has a finite mean and variance.
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