資訊工程學系(Department of Computer Science and Information Engineering)
課程名稱(英文)
Probability Theory
課程代碼
4102013_02
授課教師：
黃啟富
學分數
3
必/選修
必修
開課年級
大二上
先修科目或先備能力：
課程概述：
The goal of the course is to present probability theory in a natural way. With
interesting and instructive examples and exercises, students can easily
understand theories, definitions, theorems, and methodology. As a result, the
course materials can be connected to real-world problems
1.Sample Space
and Events
2.Axioms of
Probability
3.Basic Theorems
5. Counting
Methods
6. Independent
Trials
3
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Combinatorial
Methods
1.Counting
principle
2.Permutations 3.Combinations
4.Stirlings
Formula
4
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Conditional
Probability
and
Independence
1.Conditional
Probability
2.Law of
Multiplication
3.Law of Total
Probability
4.Bayes Formula
5.Independence
6
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The First
Midterm
Exam
1.5
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Distribution
Functions and
Discrete
Random
Variables
1.Random
Variables
2.Distribution
Functions
3.Discrete
Random
Variables
4.Expectations of
Discrete Random
Variables
5.Variances and
Moments of
Discrete Random
Variables
6.Bernoulli and
Binomial
Random
Variables
7.Poisson
Random Variable
8.Other Discrete Random
Variables
9
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Continuous
Random
Variables and
Distributions
1.Probability
Density Functions
2.Density
Function of a
Function of a
Random Variable
3.Expectations
and Variances of
Continuous
Random
Variables
4.Uniform and
Exponential
Random
Variables
5.Normal
Random Variable
6.Gamma and
Beta
Distributions
9
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The Second
Midterm
Exam
1.5
1.11.21.32.12.22.33.13.23.34.14.2
Bivariate
Distributions
1.Joint
Distribution of
Two Random
Variables
2.Independent
Random
Variables
3.Conditional
Distributions
4.Transformations
of Two Random
Variables
6
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Multivariate
Distributions
1.Joint
Distribution of
Multi
-random
Variables 2.Order Statistics
3.Multinomial
Distributions
4.Covariance and
Correlation
6
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Sum of
Independent
Random
Variables and
Limit
Theorems
1.MomentGenerating
Functions
2.Sum of
Independent
Random
Variables
3.Laws of Large
Numbers
4.Central Limit
Theorem
1.1.具有資訊工程相關基礎知識之吸收與了解的能力(Capability to grasp foundational knowledge in computer science.)
1.2.具有運用資訊工程理論及應用知識，分析與解決相關問題的能力(Capability to use computer science theory and application knowledge to analyze and solve related problems.)
1.3.在資訊工程的許多領域中，具有至少某一項專業能力，例如：硬體、軟體、多媒體、系統、網路、理論等(Professional in at least one area, including hardware, software, multimedia, system, networking, and theory.)
2.1.具有資訊工程實作技術及使用計算機輔助工具的能力(Capability to perform computer science implementations and use computer-aided tools.)
2.2.具有設計資訊系統、元件或製程的能力(Capability to design computer systems, components, or processes.)
2.3.具有科技寫作與簡報的能力。(Capability to write and present technical materials.)
3.1.具有除了已有的應用領域之外，亦可以將自己的專業知識應用於新的領域或跨多重領域，進行研發或創新的能力。(Capability to apply one’s professional knowledge to a new application domain or across multiple different application domains.)
3.2.具有領導或參與一個團隊完成一項專案任務的能力並且具有溝通、協調與團隊合作的能力。(Capability to lead or participate in group projects, with effective communication, coordination, and teamwork.)
3.3.具有因應資訊科技快速變遷之能力，培養自我持續學習之能力。(Capability to adapt to rapidly changing computer science technology and to develop self-learning capabilities.)
4.1.具有社會責任、人文素養及奉獻精神。(The awareness of social responsibilities, humanity, and contribution.)
4.2.具有工程倫理、宏觀能力、國際觀及前瞻視野。(The awareness of engineering ethics, broad capabilities, and global and contemporary vision.)