A new direct proof of the central limit theorem
نویسندگان
چکیده
منابع مشابه
A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem
The Central Limit Theorem, one of the most striking and useful results in probability and statistics, explains why the normal distribution appears in areas as diverse as gambling, measurement error, sampling, and statistical mechanics. In essence, the Central Limit Theorem states that the normal distribution applies whenever one is approximating probabilities for a quantity which is a sum of ma...
متن کاملA Computer Proof of the Central Limit Theorem
It is uncommon to apply computer algebra software to proof, especially for topics which are rarely touched by computer algebra. In order to illustrate the efficacy of symbolic computation in these respects, DERIVE is used in a statistical context to prove the Central Limit Theorem and some advantages and disadvantages of using the techniques outlined here are assessed. The proof is illustrated ...
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملThe Local Limit Theorem: A Historical Perspective
The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2017
ISSN: 0019-2082
DOI: 10.1215/ijm/1534924830