Abstract
The topic includes three chapters: the first chapter introduces the De Moive-Laplace theorem, the Lindebery-Le’vy theorem, the Lindebery theorem and the Lyapounov theorem and their proofs. Then the topic gives the limits of every central limit theorem. The third chapter talks about the usage of central limit theorems. There contains four parts: Utilizing the central limit theorem to prove complicated equality, the applications in the economic management, the applications in modern scientific calculations and the applications of to sample infer. Especially, the topic introduces a method of calculating the total value in the lottery ticket bonus, which utilizes the central limit theorem.
Keywords: central limit theorem normal distribution sample infer normal random variable
error analysis.
