# Proofs of Some Limit Theorems in Probability

### Description

This study gives detailed proofs of some limit theorems in probability which are important in theoretical and applied probability, The general introduction contains definitions and theorems that are basic tools of the later development. Included in this first chapter is material concerning normal distributions and characteristic functions, The second chapter introduces lower and upper bounds of the ratio of the binomial distribution to the normal distribution., Then these bound are used to prove the local Deioivre-Laplace limit theorem. The third chapter includes proofs of the central limit theorems for identically distributed and non-identically distributed random variables,

iii, 34 leaves

### Creation Information

Hwang, E-Bin December 1974.

### Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 26 times . More information about this thesis can be viewed below.

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• Hwang, E-Bin

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### Description

This study gives detailed proofs of some limit theorems in probability which are important in theoretical and applied probability,
The general introduction contains definitions and theorems that are basic tools of the later development. Included in this first chapter is material concerning normal distributions and characteristic functions, The second chapter introduces lower and upper bounds of the ratio of the binomial distribution to the normal distribution., Then these bound are used to prove the local Deioivre-Laplace limit theorem. The third chapter includes proofs of the central limit theorems for identically distributed and non-identically distributed random variables,

iii, 34 leaves

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#### UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

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## When

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### Creation Date

• December 1974

### Added to The UNT Digital Library

• June 24, 2015, 9:39 a.m.

### Description Last Updated

• Sept. 15, 2016, 8:34 p.m.

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