本文主要探討數學符號軟體 Mathematica 10.3 在機率分佈上的應用，介紹相關的基本指令，詳細介紹建立各種不同型態的機率分佈，以及隨機變數的重要函數的計算。
接著討論資料數據的二維圖、機率分佈的二維及三維圖，
最後使用互動式的介面介紹機率論重要的性質，如：大數法則、中央極限定理、分佈近似理論。
上述所提供的內容可以讓教師在機率分佈教學上變得更方便以及增加學生學習的效果。

This paper investigates the applications of mathematical symbolic software Mathematica 10.3 in probability distribution. The related basic
commands are illustrated. Constructing probability distributions and the calculation of important functions of a random variable are covered in details. The 2D graphs of data and the 2D and 3D graphs of probability distributions are also discussed. The important probability theorems (Law of Large Number, Central Limit Theorem,
Asymptotic Properties of Distributions) are illustrated using dynamic interactivity. It will facilitate the lecturer for teaching probability and enhance the effective learning of probability for students.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
表次 viii
第一章 前言 1
第二章 基本指令 3
2.1 List 指令 3
2.2 Abs 函數指令 4
2.3 Floor 函數指令 5
2.4 Boole 函數指令 7
2.5 Piecewise 函數指令 8
2.6 Sum 指令與 NSum 指令 10
2.7 Integrate 指令與 NIntegrate 指令 12
2.8 Simplify 指令 15
第三章 機率分佈指令 17
3.1 自訂分佈 18
3.2 參數分佈 23
3.3 非參數分佈 31
3.3.1 EmpiricalDistribution 指令 31
3.3.2 SmoothKernelDistribution 指令 34
3.3.3 HistogramDistribution 指令 36
3.4 導出分佈 38
3.4.1 MarginalDistribution 指令 39
3.4.2 TransformedDistribution 指令 50
3.4.3 ProductDistribution 指令 66
3.4.4 OrderDistribution 指令 77
3.4.5 TruncatedDistribution 指令 93
3.4.6 CensoredDistribution 指令 105
3.4.7 MixtureDistribution 指令 115
3.4.8 ParameterMixtureDistribution 指令 128
3.4.9 CopulaDistribution 指令 138
第四章 機率相關指令 148
4.1 PDF 指令 149
4.2 CDF 指令 152
4.3 Probability 指令與 NProbability 指令 155
4.4 Expectation 指令與 NExpectation 指令 162
4.5 Mean 指令 169
4.6 Variance 指令 171
4.7 Skewness 指令 174
4.8 Kurtosis 指令 177
4.9 Moment 指令 180
4.10 CetralMoment 指令 183
4.11 FactorialMoment 指令 186
4.12 Quantile 指令 189
4.13 MomentGeneratingFunction 指令 192
4.14 CentralMomentGeneratingFunction 指令 195
4.15 CumulantGeneratingFunction 指令 199
4.16 FactorialMomentGeneratingFunction 指令 202
4.17 RandomVairate 指令 205
4.18 SurvivalFunction 指令 208
4.19 HazardFunction 指令 211
第五章 統計圖表指令 214
5.1 敘述統計圖表 215
5.1.1 StemLeafPlot 指令 215
5.1.2 BoxWhiskerChart 指令 216
5.1.3 ListLinePlot 指令 218
5.1.4 Histogram 指令 219
5.1.5 SmoothHistogram 指令 222
5.1.6 ParetoPlot 指令 225
5.2 分佈統計圖表 227
5.2.1 Plot 指令 227
5.2.2 Plot3D 指令 230
5.2.3 DiscretePlot 指令 232
5.2.4 DiscretePlot3D 指令 235
5.2.5 ProbabilityPlot 指令 239
第六章 應用 242
6.1 Mathematica 指令應用 242
6.2 機率理論 246
6.2.1 大數法則 246
6.2.2 中央極限定理 248
6.2.3 分佈近似理論 250
6.3 分佈查表 253
參考文獻 258
索引 263

余玉純 (2013)。Mathematica 9.0 在機率的應用。臺灣高雄市國立中山大學碩士論文。

陳伯政(2014)。Mathematica 9.0 動態互動式功能在機率分佈的應用。臺灣高雄市國立中山大學碩士論文。

黃培芬(2012)。Mathematica 8.0 在機率與統計的應用。臺灣高雄市國立中山大學碩士論文。

Casella, George and Berger, Roger L. (2002). Statistical Inference, 2nd Edition. CA:
Thomson Learning Inc.

Mathematica 10.3 (2015). Wolfram Research.
http://www.wolfram.com/

Mathematica 10 參考資料中心 (2015). Wolfram Research, Inc. Champaign, IL.
http://reference.wolfram.com/mathematica/guide/Mathematica.html

Abs:
http://reference.wolfram.com/language/ref/Abs.html

Boole:
http://reference.wolfram.com/language/ref/Boole.html

BoxWhiskerChart:
http://reference.wolfram.com/language/ref/BoxWhiskerChart.html

CDF:
http://reference.wolfram.com/language/ref/CDF.html

CetralMoment:
http://reference.wolfram.com/language/ref/CentralMoment.html

CentralMomentGeneratingFunction:
http://reference.wolfram.com/language/ref/CentralMomentGeneratingFunction.
html

CumulantGeneratingFunction:
http://reference.wolfram.com/language/ref/CumulantGeneratingFunction.
html

DiscretePlot:
http://reference.wolfram.com/language/ref/DiscretePlot.html

DiscretePlot3D:
http://reference.wolfram.com/language/ref/DiscretePlot3D.html

Expectation:
http://reference.wolfram.com/language/ref/Expectation.html

FactorialMoment:
http://reference.wolfram.com/language/ref/FactorialMoment.html

FactorialMomentGeneratingFunction:
http://reference.wolfram.com/language/ref/FactorialMomentGeneratingFunction.
html

Floor:
http://reference.wolfram.com/language/ref/Floor.html

HazardFunction:
http://reference.wolfram.com/language/ref/HazardFunction.html

Histogram:
http://reference.wolfram.com/language/ref/Histogram.html

Integrate:
http://reference.wolfram.com/language/ref/Integrate.html

Kurtosis:
http://reference.wolfram.com/language/ref/Kurtosis.html

List:
http://reference.wolfram.com/language/ref/List.html

ListLinePlot:
http://reference.wolfram.com/language/ref/ListLinePlot.html

Mean:
http://reference.wolfram.com/language/ref/Mean.html

Moment:
http://reference.wolfram.com/language/ref/Moment.html

MomentGeneratingFunction:
http://reference.wolfram.com/language/ref/MomentGeneratingFunction.
html

NExpectation:
http://reference.wolfram.com/language/ref/NExpectation.html

NIntegrate:
http://reference.wolfram.com/language/ref/NIntegrate.html

NProbability:
http://reference.wolfram.com/language/ref/NProbability.html

NSum:
http://reference.wolfram.com/language/ref/NSum.html

ParetoPlot:
http://reference.wolfram.com/language/StatisticalPlots/ref/
ParetoPlot.html

PDF:
http://reference.wolfram.com/language/ref/PDF.html

Piecewise:
http://reference.wolfram.com/language/ref/Piecewise.html

Plot:
http://reference.wolfram.com/language/ref/Plot.html

Plot3D:
http://reference.wolfram.com/language/ref/Plot3D.html

Probability:
http://reference.wolfram.com/language/ref/Probability.html

ProbabilityPlot:
http://reference.wolfram.com/language/ref/ProbabilityPlot.html

Quantile:
http://reference.wolfram.com/language/ref/Quantile.html

RandomVariate:
http://reference.wolfram.com/language/ref/RandomVariate.html

Simplify:
http://reference.wolfram.com/language/ref/Simplify.html

Skewness:
http://reference.wolfram.com/language/ref/Skewness.html

SmoothHistogram:
http://reference.wolfram.com/language/ref/SmoothHistogram.html

StemLeafPlot:
https://reference.wolfram.com/language/StatisticalPlots/ref/
StemLeafPlot.html

Sum:
http://reference.wolfram.com/language/ref/Sum.html

SurvivalFunction:
http://reference.wolfram.com/language/ref/SurvivalFunction.html

Variance:
http://reference.wolfram.com/language/ref/Variance.html

Ross, Sheldon M. (2012). A First Course in Probability, 9th Edition. New York:
Pearson Education, Inc.

Ruskeepää, Heikki (2009). Mathematica Navigator: Mathematics, Statistics, and
Graphics, 3rd Edition. New York: Academic Press.

Wellin, Paul (2013). Programming With Mathematica. New York: Cambridge University
Press.