Seonglae ChoCLT
The phenomenon where the sum of independent random variables approaches a Normal distribution
Under certain conditions, the distribution of sample means of a sufficiently large sample size drawn from any distribution with a finite mean and variance will tend to a normal distribution, regardless of the shape of the original distribution
If you take repeated samples of size n from a population with a mean μ and a standard deviation σ, and calculate the mean of each sample, then the distribution of these means will be approximately normal with a mean of μ and a standard deviation of σ/√n, as n becomes larger
Sample Mean
Condition
Basically requires iid from any distribution with limited average and variance. However Lyapunov condition or Lindeberg condition with different variance satisfies CLT.