上课认真听讲 学习知识并非学习英语
2014-12-28
College of Computer Science & Technology, BUPT
3
Assignments

Homework Assignments

Discussions among fellow students are encouraged, but plagiarism will be dealt with seriously. Group work Discussion in classroom
Definition

Many experiments do not yield exactly the same results when performed repeatedly.


For example, if we toss a coin, we are not sure if we will get heads or tails. If we toss a die, we have no way of knowing which of the six possible numbers will turn up.
Course Staff

Instructor

杨娟 Office: 教3楼616 Phone: 62283779 Email: yangjuan@ ？？ 离散数学群：276049620

Assistants


QQ group

2014-12-28
College of Computer Science & Technology, BUPT
College of Computer Science & Technology, BUPT
5
2014-12-28
Textbook & References



Kenneth H. Rosen, Discrete Mathematics and Its Applications/7e, McGraw-Hill, 2012 Kolman B. et al, Discrete Mathematical Structures/4e, Prentice Hall, 2001 Liu, C.L. Elements of Discrete Mathematics, New York, McGrawHill, 1977 陈崇昕 等，离散数学，北京邮电大学出版社，1992 王湘浩 等，离散数学，高等教育出版社，1983 朱一清 编著，离散数学，电子工业出版社，1997 石纯一 等，数理逻辑与集合论/2e，清华大学出版社，2000 戴一奇 等，图论与代数结构，清华大学出版社，199？
2014-12-28
College of Computer Science & Technology, BUPT
15
Example


An experiment consists of drawing three coins in succession from a box containing four pennies and five dimes, and recording the sequence of results. Determine the sample space of this experiment. Solution
To:yangjuan@ College of Computer Science &
Technology
Beijing University of Posts & Telecommunications
Discrete Probability
Yang Juan
yangjuan@
2014-12-28
College of Computer Science & Technology, BUPT
12
Example

Suppose that a nickel and a quarter are tossed in the air. We describe three possible sample spaces that can be associated with this experiment.
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2014-12-28
7.1 An Introduction to Discrete Probability
Yang Juan
yangjuan@
College of Computer Science & Technology
Beijing University of Posts & Telecommunications


Experiments (10%) Midterm examination (20%) Final examination (60%)

Need a minimum of 40% of the final exam marks to pass the course! Classroom performance/behavior will be taken into consideration in assigning the final grades(10%).
College of Computer Science & Technology, BUPT
13
2014-12-28
Note




In addition to describing the experiment, we must indicate exactly what the observer wishes to record. Then the set of all outcomes of this tБайду номын сангаасpe become the sample space for the experiment. A sample space may contain a finite or an infinite number of outcomes. In this chapter, we need only finite sample spaces.
2014-12-28
College of Computer Science & Technology, BUPT
6
Please feel free to ask questions!
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Q&A
Yang Juan
yangjuan@
Comments Suggestions and

equally likely等概率 random variables 随机变量

7.2 Probability Theory


7.3 Bayes’ Theorem 7.4 Expected Value and Variance

expected value 数学期望值
College of Computer Science & Technology, BUPT


An outcome can be recorded as a sequence of length 3 constructed from the letters P (penny) and D (dime). Thus the sample space A is {PPP,PPD, PDP, PDD, DPP, DPD, DDP, DDD}.
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Course Arrangement
Yang Juan
yangjuan@
College of Computer Science & Technology
Beijing University of Posts & Telecommunications
如何使用英文教材进行学习
2014-12-28
College of Computer Science & Technology, BUPT
14
Example


Determine the sample space for an experiment consisting of tossing a six-sided die twice and recording the sequence of numbers showing on the top face of the die after each toss. Solution
College of Computer Science & Technology
Beijing University of Posts & Telecommunications
7 Discrete Probability

7.1 An Introduction to Discrete Probability
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2014-12-28
Sample Spaces(样本空间）

A set A consisting of all the outcomes of an experiment is called a sample space of the experiment.

With a given experiment, we can often associate more than one sample space, depending on what the observer chooses to record as an outcome.