2004 Yi-Ping Hung - NTU CSIE 1
科目名稱：機率（Probability）
課程編號：902-25600-01 (資工系學號單號）
授課教師： 洪一平 教授 辦公室： Room 433
Email: [email protected]
教科書： R.V. Hogg and E. A. Tanis, Probability and
Statistical Inference, 7
thed., Prentice Hall, 2006.（華泰）2004 Yi-Ping Hung - NTU CSIE 2
Course Requirement
• Homework assignments: 30%
• Lecture note: 5%
• Two in-class exams: 10%
• One midterm exam: 25%
• One final exam: 30%
2004 Yi-Ping Hung - NTU CSIE 3
Outline of the Course
1. Probability
2. Discrete Distributions 3. Continuous Distributions 4. Multivariable Distributions 5. Sampling Distribution Theory 6. Estimation
7. Bayesian Methods
8. Test of Statistical Hypotheses
9. Theory of Statistical Tests10. Quality Improvement Through Statistical Methods
2004 Yi-Ping Hung - NTU CSIE 4
Chapter 1 Probability
• Basic Concepts
• Mean, Variance, Standard Deviation
• Axioms and Properties of Probability
• Methods of Enumeration
• Conditional Probability
• Independent Events
• Bayes’ Theorem
2004 Yi-Ping Hung - NTU CSIE 5
1.1 Basic Concepts
• Statistics
– data Æ information Æ decision
– need probability(mathematical background)
• Variation is almost everywhere
– probabilistic models for the variation
• Probability and Statistics are extremely useful
– highly desirable for graduate work in many areas
2004 Yi-Ping Hung - NTU CSIE 6
Example 1.1-9
S: Outcome space, Sample space, Space
f
: frequency of the outcomen : number of trials
f / n
: relative frequency of the outcome Simpson’s Paradox2004 Yi-Ping Hung - NTU CSIE 7
Frequency table
2004 Yi-Ping Hung - NTU CSIE 8
Histogram: Relative Frequency Histogram
2004 Yi-Ping Hung - NTU CSIE 9
Example 1.1-10
S = {1, 2, 3}
f(x) : probability mass function, p.m.f.
f(1) = 3/6, f(2) = 2/6, f(3) = 1/6,
h(1) = 284/600, f(2) = 208/600, f(3) = 108/600,
2004 Yi-Ping Hung - NTU CSIE 10
Chapter 1
Empirical and Probability Distributions
• Basic Concepts
• Mean, Variance, Standard Deviation
• Continuous-Type Data
• Exploratory Data Analysis
• Graphical Comparisons of Data Sets
• Time Sequences
• Probability Density and Mass Functions
2004 Yi-Ping Hung - NTU CSIE 11
1.2 Mean, Variance, Standard Deviation
• Mean
of the random variable X (or of its distribution)• Variance
of the random variable X (or of its distribution)- second moment about the mean
平均數
變異數
Standard deviation
標準差
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• Performa a certain random experiment n times obtaining n observed values of the random variable, say x1, x2, …, xn. Æ sample
• Empirical distribution: determined by the data
x1, x2, …, xn.• mean of the empirical distribution
• sample mean
樣本平均數2004 Yi-Ping Hung - NTU CSIE 13
• Variance of the empirical distribution
