I’m not sure if you meant short note or "short" note, but this is a "short" note

prob. theory central limit theorem (clt) states conditions with mean sufficiently large numer, independent random variables, finite mean and variance, approx. normal distributed clt requires random variables

Central limit theorem is an important principle of statistics, which states that probability distribution of a large number of independent repeated events is represented by normal distribution of statistics. Because of type of behaviour displayed by probability distribution of all types of probability distributions, the mean of the means of sample drawn from a population will equal the population mean regardless of the sample size. Also as the sampling distribution of the mean will approach normality, regardless of the shape of the population distribution.

Because of this kind of relationship that exists between any type of statistical distribution and normal distribution, it is possible to draw inferences about an entire population based on observation of a sample drawn from the population., without knowing anything about the shape of the probability curve of the population under study.