Central Limit Theorem - Central Limit Theorem

Central Limit Theorem - Central Limit Theorem

Central limit theorem of probability theory refers to the sequence of random variables discussed in section and distribution of a class of theorems on asymptotic normal distribution. Central limit theorem is the theoretical basis of mathematical statistics and error analysis, pointing out the large number of conditions approximate normal distribution of random variables. In nature and production, some of the phenomena influenced by many independent random factors, if the impact of each factor generated are tiny, the overall effect can be seen as the normal distribution. Central Limit Theorem is proved that this phenomenon mathematically.

According to the central limit theorem, when the sample size is large, the sampling distribution of population parameters that tend to be normally distributed, it can eventually be tested further analysis based on the normal distribution formula.

Central Limit Theorem, in theory, to ensure that we can use only part of the sampling method, the purpose of the study speculated that the statistical parameters.

Approximately equal to the overall mean of the sample average. No matter what the overall distribution of any of the overall sample mean will surround the whole overall average and normally distributed.

Each time capacity is drawn from the population $n$ simple random sample, if the sample size is large, the sampling distribution of the sample mean of the normal distribution approximation (desirably $\ mu$ , standard deviation $\frac{\sigma}{\sqrt{n}}$)。