| 課程大綱 Syllabus |
學生學習目標
Learning Objectives |
單元學習活動
Learning Activities |
學習成效評量
Evaluation |
備註
Notes |
序
No. | 單元主題
Unit topic |
內容綱要
Content summary |
| 1 | Combinatorial Analysis |
Introduction
The Basic Principle of Counting
Permutations
Combinations
Multinomial Coefficients
The Number of Integer Solutions of Equations |
了解學習機率前所需了解之相關計數技巧 |
|
|
|
| 2 | Axioms of Probability(I) |
Introduction
Sample Space and Events
Axioms of Probability
Some Simple Propositions |
了解何謂樣本空間、事件、機率公設及其延伸命題。 |
|
|
|
| 3 | Axioms of Probability(II) |
Sample Spaces Having Equally Likely Outcomes
Probability As a Continuous Set Function
Probability As a Measure of Belief |
了解古典機率、客觀機率、主觀機率等機率理論異同及適用時機 |
|
|
|
| 4 | Conditional Probability and Independence(I) |
Introduction
Conditional Probabilities
Bayes' Formula |
了解何謂條件機率及其使用時機、何謂貝氏定理及其應用 |
|
|
|
| 5 | Conditional Probability and Independence(II) |
Independent Events
P(．|F) is a Probability |
了解何謂統計獨立事件以及應用 |
|
|
|
| 6 | Random Variables(I) |
Random Variables.
Discrete Random Variables
Expected Value
Variance |
1.了解何謂隨機變數及為何要學習隨機變數
2.了解何謂離散隨機變數
3.了解何謂期望值及變異數及其計算方式與應用 |
|
|
|
| 7 | Random Variables(II) |
Discrete Probability Distribution:
Bernoulli, Binomial and Geometric Random Variables |
了解學習常見離散機率分布中與伯努利隨機過程相關的伯努利分布、二項分布、幾何分布、負二項分布， 並知道如何應用於日常生活 |
|
|
|
| 8 | Random Variables(III) |
Discrete Probability Distribution:
Negative Binomial, Hypergeometric Random Variables |
了解學習常見離散機率分布中的負二項分布、超幾何分布, 並知道如何應用於日常生活 |
|
|
|
| 9 | 期中考 |
Ch1~Ch4(4.6) |
複習Ch1~Ch4(4.6)所學 |
|
|
|
| 10 | Random Variables(IV) |
Discrete Probability Distribution:
Poisson Random Variables |
了解學習常見離散機率分布中的卜瓦松分布, 並知道如何應用於日常生活 |
|
|
|
| 11 | Random Variables(V) |
Expected Value of Sums of Random Variables
Properties of the Cumulative Distribution Function |
1.了解如何計算隨機變數之和的期望值
2.了解累積機率分配及其計算方式與應用 |
|
|
|
| 12 | Continuous Random Variables(I). |
Introduction
Expectation and Variance of Contunuous Random Variables |
了解何謂連續隨機變數、機率密度函數，並學會如何計算連續隨機變數的期望值及變異數 |
|
|
|
| 13 | Continuous Random Variables(II). |
Continuous Distributions(Normal Distribution) |
學會常見之連續隨機變數分布，如常態分布、指數分布等。 |
|
|
|
| 14 | Continuous Random Variables(III). |
Continuous Distributions(Exponential Distribution) |
學會常見之連續隨機變數分布，如常態分布、指數分布等。 |
|
|
|
| 15 | Continuous Random Variables(IV). |
Other Continuous Distribution:
Gamma and Weibull Distributions |
了解其它常見連續分布, 如珈瑪分布、韋布分布及其應用 |
|
|
|
| 16 | Continuous Random Variables(V). |
The Distribution of a Function of a Random Variable |
連續隨機變數之變數變換 |
|
|
|
| 17 | Jointly Distributed Random Variables |
Joint Distribution Functions
Independent Random Variables
Conditional Distributions
Order Statistics |
了解多變數之機率分布及其相關性質 |
|
|
|
| 18 | 期末考 |
Ch4(4.7)~Ch6 |
複習Ch4(4.7)~Ch6所學 |
|
|
|