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： 九十七學年 第一學期 | 授課班 級： 數學系三 | |
| 全/半年： 半 | 必/選修：必 | 學分： 3 |
| 上課時間：星期四下午 2:10 至 5:00 | 上課地點： | |
| 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/prob97/index.html | ||
| E-mail: pwtsai@math.ntnu.edu.tw | ||
| 助教姓名： | 助教 Office Hours： | |
| 助教聯絡方式：數學館 M 410 | ||
| HT | ||
| 1. Combinatorial
Analysis |
(a) Counting
techniques:
multiplication principle, permutations,
combinations (b) Multinomial Coefficients |
1.3 |
| 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. |
1.1 1.2 |
| 3. Conditional probability | (a)
Conditional probability (b) Bayes’ Formula (c) Independent events |
1.4 1.5 1.6 |
| 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, Uniform Distribution, Geometric Distribution, Negative Binomial Distribution, Hypergeometric Distribution, Poisson Distribution, (f) Poisson approximation to the Binomial (g) The moment generating function |
ch2 |
| Midterm
exam |
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| 5.Continuous Distribution | (a)
Continuous-type data (b) Some continuous distribution: Uniform Distribution, Exponential Distribution, Normal Distribution, Cauchy Distribution (c) Gamma and Chi-square Distribution (d) Normal approximation to the binomial |
ch3 5.1 5.2 5.5 |
| quiz 1 (1 hr) |
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| 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 (f) Distributions of functions of a random variable: Normal to Chi-square Distribution, Lognormal |
4.1 4.2 4.3 4.4 4.5 |
| quiz 2 (1 hr) |
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| 7. Expectation | (a)
Expectation of sums of r.v.s (b) Covariance, Variance of sums, Correlations (c) Conditional expectation (d) More one Normal Distribution |
4.6 5.3 5.6 |
| 8. Limit laws | (a)
Chebyshev’s inequality (b) Strong law of large numbers, Weak law of large numbers (c) The Central Limit Theorem |
4.7 5.4 |
| Final exam |
| Lecture notes | HW |
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| 9/18 |
Ch1.pdf |
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| 9/25 |
hw97_1.pdf
(due 10/2) 9/25修正後 |
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| 10/2 |
Ch2.pdf | hw97_2.pdf
(due 10/9) |
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| 10/9 |
2.1-3(a,d), , 2.1-11., 2.2-2, 2.2-10 2.3-13 2.3-14 |
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| 10/16 |
2.4-3, 2.4-6, 2.4-10 2.4-23 2.5-2 (a) (d), 2.5-4, 2.5-8 2.5-10, 2.5-11, 2.5-21 |
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| 10/23 |
HW: due 2-1 ~ 2-5 | 2.6-3, 2.6-4, 2.6-8, 2.6-10 | ||
| 10/30 |
期中考 |
mid1.pdf |
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| 11/6 |
Ch3.pdf some graphs |
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| 11/13 |
3.2-3.3 and 3.4 gamma | 3.2-1(c), 3.2-6, 3.2-8 3.3-3, 3.3-4, 3.3-5, 3.3-10, 3.4-7, 3.4-8, 3.4-12 |
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| 11/20 |
3.4 Chi-square 3.5, 5.2 | |||
| 11/27 |
小考 3.3, 3.4, 3.5, 5.2 Ch401.pdf |
3.4-11, 3.4-16, 5.2-11, 5.2-18(b) 3.5-2, 3.5-10, 3.5-11 5.2-5(b), 5.2-6(c), 5.2-10, 5.2-24, 5.2-26 |
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| 12/4 |
Ch402.pdf | |||
| 12/11 |
Ch403.pdf | 4.1-1, 4.1-9, 4.1-12 4.2-3(a),(b), 4.2-7, 4.2-8(b), (c), (d). 4.2-12 (a) (b) 4.3-1(e) 4.4-13(d) 4.3-16(c) (due 12/11) |
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| 12/18 |
4.4-1, 4.4-8, 4.4-14 4.5-2, 4.5-3, 4.5-6, 4.5-7, 4.5-9, 4.5-15. (due 12/30) |
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| 12/25 |
小考 4.1-4.4 請看講義範圍 ch401.pdf & ch402.pdf quiz2_sol.pdf |
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| 1/1 |
4.6-1, 4.6-6, 4.6-26 4.7-1(a), 4.7-6, 5.2-17, 5.3-3, 5.3-5, 5.3-6 (due 1/8) |
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| 1/8 |
Ch5.pdf | 5.3-8(b) 5.3-14, 5.3-18 5.4-10,
5.4-14. 5.5-1, 5.5-8, 5.5-11, 5.5-22 (no need to hand in) |
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| 1/15 |
期末考 |