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《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