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 th
ed., Prentice Hall, 2006.（華泰）Course Requirement
• Homework assignments: 30%
• Lecture note: 5%
• Two in-class exams: 10%
• One midterm exam: 25%
• One final exam: 30%
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
Chapter 1 Probability
• Basic Concepts
• Mean, Variance, Standard Deviation
• Axioms and Properties of Probability
• Methods of Enumeration
• Conditional Probability
• Independent Events
• Bayes’ Theorem
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
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 ParadoxFrequency table
Histogram: Relative Frequency Histogram
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,
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
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
• Performa a certain random experiment n times obtaining n observed values of the random variable, say x
1
, 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• Variance of the empirical distribution
