Download Introduction of Course

《概率与统计》双语课程教学大纲
1. Introduction of Course
The probability & statistics is a science of studying statistic law of random
phenomena . This science generated from 17th century, it comes of gambling and is
applied in gambling. But now it is the foundation of many sciences, for example,
econometrics, control science, information science, decision theory, game theory. This
course will mainly introduce probability base concepts and statistics base methods to
students, including the Concept of Probability, Random Variables, Distribution
Function, Density Function, Expectation, Variance, Independence, Conditional
Probability, Special Discrete Models, Special Continuous Models, the Concept of
Statistics, Sampling Distributions, Parameter Estimation, Hypothesis Testing,
Linear Regression, and so on.
2.Applications in Business and Economics•Accounting
Public accounting firms use statistical sampling procedures when conducting
audits for their clients. For instance, suppose an accounting firm wants to determine
whether the amount of accounts receivable shown on a client’s balance sheet fairly
represents the actual amount of accounts receivable. Usually the number of individual
accounts receivable is a large that reviewing and validating every account would be
too time-consuming and expensive. The common practice in such situations is for the
audit staff to select a subset of the accounts called a sample. After reviewing the
accuracy of the sampled accounts, the auditors draw a conclusion as to whether the
accounts receivable amount shown on the client’s balance sheet is acceptable. •
Finance
Financial advisors use a variety of statistical information to guide their
investment recommendations. In the case of stocks, the advisors review a variety of
financial data including price/earnings ratios and dividend yields. By comparing the
information for an individual stock with information about the stock market averages,
a financial advisor can begin to draw a conclusion as to whether an individual stock is
over or undervalued. For example, Barron’s reported that the average price/earnings
ratio for the 30 stocks in the Dow Jones Industrial average was 22.0. Philip Morris
had a price/earnings ratio of 16.9. In this case, the statistical information on
price/earnings ratios showed that Philip Morris had a lower price in comparison to its
earnings than the average for the Dow Jones stocks. Therefore, a financial advisor
might have concluded that Philip Morris was currently underpriced. This and other
information about Philip Morris would help the advisor make buy, sell, or hold
recommendations foe the stock.
•Marketing
Electronic scanners at retail checkout counters are being used to collect data for a
variety of marketing research applications. For example, data suppliers such as A.C.
Nielesen and Information Resources, Inc., purchase point-of-sale scanner data from
grocery stores, process the data, and then sell statistical summaries of the data to
manufactures. Manufacturers spent an average of $387,325 per product category to
obtain this type of scanner data. Manufactures also purchase data and statistical
summaries on promotional activities such as special pricing and the use of in-store
displays. Brand managers can review the scanner statistics and the promotional
activity statistics to gain a better understanding of the relationship between
promotional activities and sales. Such analyses are helpful in establishing future
marketing strategies for the various products.
•Production
With today’s emphasis on quality, quality control is an important application of
statistics in production. A variety of statistical quality control charts are used to
monitor the output of a production process. In particular, an x-bar chart is used to
monitor the average output. Suppose, for example, that a machine is being used to fill
containers with 12 ounces of a well-known soft drink. Periodically, a sample of
containers is selected and the average number of ounces in the sample containers is
computed. This average, or x-bar value, is plotted on an x-bar chart. A plotted value
above the chart’s upper control limit indicates overfilling, and a plotted value below
the chart’s lower control limit indicates underfilling. The process is termed “in
control” and allowed to continue as long as the plotted x-bar values are between the
chart’s upper and lower control limits. Properly interpreted, an x-bar chart can help
determine when adjustments are necessary to correct a production process.
•Economics
Economists are frequently asked to provide forecasts about the future of the economy or
some aspect of it. They use a variety of statistical information in making such forecasts. For
instance, in forecasting inflation rates, economists use statistical information on such indicators as
the Producer Price Index, the unemployment rate, and manufacturing capacity utilization. Often
these statistical indicators are entered into computerized forecasting models that predict inflation
rates.
3. Course Contents
Chapter 1 Probability
1.1 Introduction
1.2 Sample Space
1.3 Probability Measures
1.4 Computing Probabilities: Counting Methods
1.5 Conditional Probability
1.6 Independence
1.7 Concluding Remarks
Chapter 2 Random Variables
2.1 Discrete Random Variables
2.2 Continuous Random Variables
2.3 Functions of a Random Variable
2.4 Concluding Remarks
Chapter 3 Joint Distributions
3.1 Introduction
3.2 Discrete Random Variables
3.3 Continuous Random Variables
3.4 Independent Random Variables
3.5 Conditional Distributions
3.6 Functions of Joint Distributed Random Variables
3.7 Extrema and Order Statistics
Chapter 4 Expected Values
4.1 The Expected Value of a Random Variable
4.2 Variance and Standard Deviation
4.3 Covariance and Correlation
4.4 Conditional Expectation and Prediction
4.5 The Moment-Generating Function
4.6 Approximate Methods
Chapter 5 Limit Theorems
5.1 Introduction
5.2 The Law of Large Numbers
5.3 Convergence in Distribution and the Central Limit Theorem
Chapter 6 Distributions Derived from the Normal Distribution
6.1 Introduction
6.2 x2,t, and F Distributions
6.3 The Sample Mean and the Sample Variance
Chapter 7 Estimation of Parameters and Fitting of Probability Distributions
7.1 Introduction
7.2 Fitting the Poisson Distribution to Emissions of Alpha Particles
7.3 Parameter Estimation
7.4 The Method of Moments
7.5 The Method of Maximum Likelihood
7.6 Efficiency and the Cramer-Rao Lower Bound
7.7 Sufficiency
Chapter 8 Testing Hypotheses and Assessing Goodness of Fit
8.1 Introduction
8.2 The Neyman-Pearson Paradigm
8.3 Optimal Tests: The Neyman-Pearson Lemma
8.4 The Duality of Confidence Intervals and Hypothesis Tests
8.5 Generalized Likelihood Ratio Tests
8.6 Likelihood Ratio Tests for the Multinomial Distribution
8.7 The Poisson Dispersion Test
8.8 Hanging Rootograms
8.9 Probability Plots
8.10 Tests for Normality
Chapter 14 Linear Least Squares
14.1 Introduction
14.2 Simple Linear Regression
14.3 The Matrix Approach to Linear Least Squares
14.4 Statistical Properties of Least Squares Estimates
14.5 Multiple Linear Regression-An Example
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap
4. Course Scheming
Chapters
Chapter 1 Probability
Chapter 2 Random Variables
Chapter 3 Joint Distributions
Chapter 4 Expected Values
Chapter 5 Limit Theorems
Chapter 6 Distributions Derived from the
Normal Distribution
Chapter 7 Estimation of Parameters and
Fitting of Probability Distributions
Chapter 8 Testing Hypotheses and
Assessing Goodness of Fit
Chapter 14 Linear Least Squares
5 Course Test
The first examination (10%), chapter 1 to chapter 3
The medium examination (10%), chapter 1 to chapter 5
The second examination (10%), chapter 6 to chapter 8
The final examination (50%), chapter 1 to chapter 8
Daily work (once a week) (10%)
Attendances (10%)
Classes Hours
12
10
6
10
2
2
8
8
6