國 立台灣師範大學數 學系教學大綱

授課教師：蔡碧紋   助理教授

課程名稱 （中文）：機率導論

（英文）：Introduction to Probability

學年： 九十八學年 第二學期 授課班 級： 數學系三
全/半年： 半 必/選修：必 學分： 3
上課時間：星期五上午9:00 至 12:00 上課地點： C004
教師聯絡方式：數學館 M205 Office Hours: 週三 9-11
教學網頁：http://math.ntnu.edu.tw/~pwtsai/prob9802/index.html
E-mail: pwtsai@math.ntnu.edu.tw
助教姓名：林炯伊 助教 Office Hours：星期五 12:30-1:30 (M407)
助教聯絡方式：數學館 M 410


New: 學期成績


一、教學目標：

本課程介紹機率論的基本概念和基本極限理論，並引導學生發掘機率的奧秘。


二、教材內容及進度規劃：

書目: Ross, S. (2009) A First Course in Probability 8th ed. Pearson Prentice Hall (華泰書局代理);


HW
 Lecture Notes
 Problems
 Exercises
 Self-Test
ch1 prob9802_1.pdf
 10,26,31
 13
 6
ch2
2,25,28,47,52
 3,20
 14
ch3
6,12,13,14,43,67,79,84
 28
 23
ch4
5,6.17,20,25,28,35,38,49,52,58,59
 4,7, 7.48
 5,15,24


Midterm I (4/16)暫定 Ch1-4+7.7
ch5
 prob9802_2.pdf 2,8,13,14,19,20,28,32,37,39,40,
7,29,30
 5
ch6
1,10,13,17,19,21,22,27,40,42,56
 9,14,
 15


改 為(5/14) 1小時的小考 範圍暫定 Ch5+10.2.1
改為(6/4) 1小時的小考 範圍暫定 Ch6
ch7
 prob9802_3.pdf
 4, 11,16,26,30, 33,40,49,65,72, 75
 10,

ch8
2-4,13,



Final (6/18)
Ch5, 6 (6.6,6.8不考) 7, (7.3, 7.5.4, 7.9 不考)
8.1-8.3


Syllabus

1. Combinatorial Analysis

                        (a) Counting techniques: multiplication principle, permutations, combinations,

                        (b) Multinomial Coefficients
 

2. Probability: Set theory

                        (a) Probability set up: sample space, event

                        (b) axioms and some propositions

                        (c) What is probability? equally likely, relative frequency, a measure of belief. 

3. Conditional probability and Independence

                        (a) Conditional probability

                        (b) Bayes’ Formula

                        (c) Independent Events
 

4. Random variables

                        (a) What is random variables

                        (b) Cumulative distribution function

                        (c) Discrete R.V.s

                        (d) The Mean, variances and standard deviation

                        (e) Some discrete distributions:
                    Bernoulli trials, Binomial Distribution, Poisson Distribution
                    Geometric Distribution, Negative Binomial Distribution,
                    Hypergeometric Distribution,

                        (f) Moment generating functions (7.7)

                        (g) Poisson approximation to the Binomial


Mid-term I
 

5. Continuous Distribution

                        (a) Continuous-type data

                        (b) Some continuous distribution: Uniform Distribution, Exponential Distribution, Normal Distribution

                        (c) Gamma and Chi-square Distribution

                        (d) Normal approximation to the binomial

                        (e) Distributions of functions of a random variable: Normal → Chi-square Distribution, Lognormal
 

6. Jointly Distributed R.V.s

                        (a) Joint Distribution

                        (b) Independent r.v.s

                        (c) Sums of Independent r.v.s

                        (d) Conditional Distribution

                        (e) Joint Distribution of Functions of Random Variables

 
        Mid-term II

7. Expectation

                        (a) Expectation of sums of r.v.s

                        (b) Moments

                        (c) Covariance, Variance of sums, Correlations

                        (d) Conditional expectation

                        (f) More one Normal Distribution

 

8. Limit laws

                        (a) Chebyshev’s inequality

                        (b) Strong law of large numbers, Weak law of large numbers

                        (c) The Central Limit Theorem

        Final exam
 
三、   實施方式：

課堂講授

 

四、   評量標準與成績計算方式：Max(A, B)

A. 三次考試各佔 30%, 30%(二次小考）, 50%  (100/110)
               or  35%,  30%(二次小考）, 45%  (100/110)

B. 作業+隨 堂小考+平時成績 15%, 三次考試各佔 30%, 25%(二次小考）, 40% (100/110)

五、   參考 書目：

Hogg, R.V. & Tanis, E. A. (2006) Probability and Statistical Inference, 7th edition, Prentice Hall.

陳旭昇（2007) 統計學：應用與進階 （東華出版）

   國內相 關網站

中山大學應用數學系機率網路學習館 http://eprob.math.nsysu.edu.tw/