Probability and Statistics


 date:2010-1-7 12:05:00 source:BiMBA         

References:

De'en Gong: Basic Mathematics for Economists --- Probability and Statistics, Sichuan People's Publishing House, Sichuan, 2000(Teaching Material)

Jiading Chen, Wanru Liu, Rengong Wang: The Lectures of Probability and Statistics, Higher Education Press, Beijing, 2004

Structure of the Course:

1.       Random Event and Probability

1.1   Random Event and Probability

1.2   Classical Probability and geometric Probability

1.3   Conditional Probability and Independence of Events

1.4   Complete Probability Formula and Bayes Formula

1.5   Binomial Probability

2.       Distribution of random variables function

2.1   Discrete probability distribution

2.2   Continuous probability distribution and its probability density

2.3   Other commonly used Distribution of random variables

2.4   Distribution of random variables function

3.       Mathematical Expectation and Variance of random variables

3.1   Mathematical Expectation of random variables

3.2   Variance of random variables

3.3   Mathematical Expectation and Variance of commonly used random variables

4.       Distribution of random Vectors and its mathematical Expectation and Variance

4.1   Joint Distribution of two-dimensional random Vectors

4.2   Marginal Distribution of two-dimensional random Vectors and its Independence

4.3   Mathematical Expectation and Variance of two-dimensional random Vectors Function

4.4   Covariance and Correlation Coefficient of two-dimensional random Vectors

4.5   Distribution, Independence, mathematical Expectation and Variance, Covariance and Correlation Coefficient of n-dimensional random Vectors

4.6   Law of large numbers and central limit Theorem

5.       Statistical Estimation

5.1   Random of random Sampling

5.2   Mathematical Expectation and Variance of Point Estimation

5.3   Confidence Interval of mathematical Expectation

5.4   Confidence Interval of Variance

5.5   Maximum Likelihood Estimation

6.       Hypothesis test

6.1   Problem Formulation and reduction to absurdity of the nature of a Probability

6.2   Hypothesis test for mathematical Expectation of a normal Population

6.3   Hypothesis test for Variance of a normal Population

6.4   Hypothesis test of two normal Populations

7.       Regression Analysis

7.1   Empirical Equation of simple linear Regression

7.2   Significance Testing of simple linear Regression Effect

7.3   Linearisation of nonlinear Problem

Course Objectives:

1.  Develop skills in understanding and applying basic statistical methods.

2.  Develop an appreciation for the use of statistics in decision making, and an appreciation of its limitations.

3.  Develop an ability to use computers and/or calculators for statistical analysis of data.

Examination:

Regular attendance, participation, lab activities, quizzes, homework: 30%

Mid –Term Test: 30%

Final Test: 40%

Credits & Workload:

3 Credits & 4 hours per Week (teaching) + 2 hours per Week (tutoring); 12 Weeks, 48 hours (teaching) + 24 hours (tutoring)

Excerpt:

The introductory remark of my teacher ------ Probability and Statistics are as much about intuition and problem solving, as they are about theorem proving. Because of this, you can find it very difficult to make a successful transition from lectures to examinations to practice, since the problems involved can vary so much in nature. Since the subject is critical in many modern applications such as mathematical finance, quantitative management, telecommunications, signal processing, bioinformatics, as well as traditional ones such as insurance, social science and engineering, I have rectified deficiencies in traditional lecture-based methods by collecting together a wealth of exercises for which they have supplied complete solutions. These solutions are adapted to needs and skills of you.

 
 
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