Probability and Statistics1Textbook and ReferencesTextbook: Jay L. Devore, Probability and statistics for engineering and the sciences (6th ed.), 机械工业出版社, ISBN 7-111-15724-9.References:茆诗松、程依明、濮晓龙，概率论与数理统计教程，北京：高等教育出版社，2004，ISBN 7-040-14365-2R. Johnson, Miller & Freunds Probability and Statistics for Engineers, 7th Ed. Pearson Education, 2005, ISBN 0-131-43745-6影印改编版：章栋恩改编，概率论与数理统计（第7版），北京：电子工业出版社，2005，ISBN 7-121-01931-0盛骤、谢式千、潘承毅，概率论与数理统计（第4版），北京：高等教育出版社，2008，ISBN 7-040-23896-92Why study probability and statistics?The only purposeful impact you will have on your life and in the world will come from decisions you make.What makes decisions hard?One thing that makes decisions hard is uncertainty.3Why study probability and statistics?We are able to explicitly include uncertainty into decision making using probability.What happens if you ignore uncertainty in decision making?4What do we do when faced with uncertainty?How do you design a policy for climate change?How do you design a culvert for flood prevention?Plan for the “worst case”?Plan for the “average case?”5ExamplesPlanning and design of airport pavementThicker lasts longerThicker more expensiveRelation between thickness and life is uncertain.Therefore, the total cost of the project is uncertain.6ExamplesDesign of an offshore drilling towerHow safe is safe enough?Possibility of hurricane during useful life7Design of an off-shore wind turbinefatigue life is unknownmust design to tradeoff initial costs with lifetime and reliability8What is probability?Uncertainty can be assessed or discussed informally using language such as “it is unlikely” or “probably”.Probability measures uncertainty formally, quantitatively. It is the mathematical language of uncertainty.It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. Pierre-Simon Laplace, Thorie Analytique des Probabilits, 1812.9What is statistics?Statistics provide data about uncertain relationships. They are numbers that summarize the results of a study.Statistical inference formalizes the process of learning through observation.Statistics is the field that studies how to efficiently collect informative data, explore and interpret these data and draw conclusions based on them.10Chapter 1 Overview and Descriptive Statistics1.1 Populations, Samples, and Process1.2 Pictorial and Tabular Methods in Descriptive Statistics1.3 Measures of Location1.4 Measures of Variability 11Introduction Statistical concepts and methods are not only useful but indeed often indispensable in understanding the world around us. They provide ways of gaining new insights into the behavior of many phenomena that you will encounter in your chosen field of specialization on engineering or science. The probability & statistics is a science of studying statistic law of random phenomena. This science is generated from 17th century, comes of gambling and is applied in gambling.But now it is the foundation of many sciences, for example, computer science, information science, communication engineering, control science, decision theory, game theory, econometrics, etc.12This course will mainly introduce probability basic concepts and statistics basic 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, and so on.131.1 Populations, Samples, and Processes Engineers and scientists are constantly exposed to collections of facts, or data, both in their professional capacities and in everyday activities. The discipline of statistics provides methods for organizing and summarizing data, and for drawing conclusions based on information contained on the data. A population（总总体体） an investigation will typically focus on a well-defined collection of objects . A population is the set of all elements of interest in a particular study.For example: (1) All gelatin capsules of a particular type produced during a specified period. (2) All individuals who received a B.S. in engineering. (3) All students whos mathematics score above 70. 14Sample（样本）（样本） A sample is a subset of the population.Population = group of people/objects that you really want to know about, e.g., shipment of light bulbsSample = the group of people/objects you are actually able to examine, e.g., 5 light bulbsProbability: If 10% of the light bulbs are defectives, how many will I expect to see in my sample?Statistics: If I have 1 bad light bulb in my sample, is that strong enough evidence to convince me to not take the shipment?15PopulationSample16 Data Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation. Together, the data collected in a particular study are referred to as the data set for the study. Table 1.1 shows a data set containing financial information for some companies, taken from the Stock Investor Pro database.companyexchangeTicker symbolAnnual salesShare pricePrice/earnings ratioAward softwraeOTCAWRD15.711.50022.5Chesapeake energyNYSECHK255.37.88012.7Craig corporationNYSECRG29.417.0007.5EdistoAMEXEDT254.69.6886.017Elements, Variables , and Observations The elements are the entities on which data are collected. For the data in table1.1, each company is an element. A variable is a characteristic of interest for the elements. x = gender of a graduating engineer y = number of major defects on a newly manufactured automobile z = braking distance of an automobile under specified conditions A univariate（单变）data set consists of observations on a single variable Bivariate（双变）data means observations are made on each of two variables. The set of measurements collected for a particular element is called an observation（观察值）.18 Branches of StatisticsDescriptive statistics（描述性统计）（描述性统计） An investigator who has collected data may wish simply to summarize and describe important features of the data. This entails using methods from descriptive statistics. Some of these methods are graphical in nature; the construction of histograms（直方图）, boxplots（箱线图）, and scatter plots（散点图）are primary examples. Other descriptive methods involve calculation of numerical summary measures, such as means, standard deviations, and correlations coefficients.19Example 1.1 Here is data consisting of observations on x = O-ring temperature for each test firing or a actual launch of the shuttle rocket engine253545556575852010304020 Inferential statistics（推断统计）（推断统计）A major contribution of statistics is that data from a sample can be used to make estimates and test hypotheses about the characteristics of a population. This process is referred to as statistical inference （统计推断）.For example: (1) 10 of last years engineering graduates to obtain feedback about the quality of the engineering curricula.(2) A sample of bearings from a particular production run.21Example 1.2 Material strength investigations provide a rich area of application for statistical methods. Suppose we have the following data on flexural strength:5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7Now we want an estimate of the average value of flexural strength for all beams that could be made in this way. It can be shown that, with a high degree of confidence, the population mean strength is between 7.48 Mpa and 8.80 Mpa; we call this a confidence interval（置信区间）or interval estimate（区间估计）. 22 In a probability problem, properties of the population under study are assumed known, and questions regarding a sample taken from the population are posed and answered. In a statistics problem, characteristics of a sample are available to the experimenter, and this information enables the experimenter to draw conclusions about the population. The relationship between the two disciplines can be summarized by saying that probability reasons from the population to the sample, whereas inferential statistics reasons from the sample to the population.populationsampleprobabilityinferential statistics231.Population consists of all bulbs2.A sample of 200 bulbs is manufactured with the new filament 3.The sample data provides a sample average lifetime of 76 hours per bulb 4.The value of the sample average is used to make an estimate about the population averageAnother example: To estimate the lifetime of some kind of bulbs.24 Enumerative Versus Analytic Studies An enumerative study is focused on a finite, identifiable, unchanging collection of individuals or objects that make up a population. An analytic study is broadly defined as one that is not enumerative in nature. Such studies are often carried out with the objective of improving a future product by taking action on a process of some sort. 25