概率論與數(shù)理統(tǒng)計(jì)lec011.1

1、probability and statisticstextbook and references textbook: jay l. devore, probability and statistics for engineering and the sciences (6th ed.), 機(jī)械工業(yè)出版社, isbn 7-111-15724-9. references: 茆詩松、程依明、濮曉龍，概率論與數(shù)理統(tǒng)計(jì)教程，北京：高等教育出版社，2004，isbn 7-040-14365-2 r. johnson, miller & freunds probability and statis

2、tics for engineers, 7th ed. pearson education, 2005, isbn 0-131-43745-6影印改編版：章棟恩改編，概率論與數(shù)理統(tǒng)計(jì)（第7版），北京：電子工業(yè)出版社，2005，isbn 7-121-01931-0 盛驟、謝式千、潘承毅，概率論與數(shù)理統(tǒng)計(jì)（第4版），北京：高等教育出版社，2008，isbn 7-040-23896-9why study probability and statistics? the only purposeful impact you will have on your life and in the world

3、will come from decisions you make. what makes decisions hard? one thing that makes decisions hard is uncertainty.why 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?what d

4、o 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?”examples planning and design of airport pavement thicker lasts longer thicker more expensive relation between t

5、hickness and life is uncertain. therefore, the total cost of the project is uncertain.examples design of an offshore drilling tower how safe is safe enough? possibility of hurricane during useful life design of an off-shore wind turbine fatigue life is unknown must design to tradeoff initial costs w

6、ith lifetime and reliabilitywhat 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

7、 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.what is statistics? statistics provide data about uncertain relationships. they are numbers that summarize the results of a

8、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.chapter 1 overview and descriptive statistics1.1 populations, sam

9、ples, and process1.2 pictorial and tabular methods in descriptive statistics1.3 measures of location1.4 measures of variability introduction statistical concepts and methods are not only useful but indeed often indispensable in understanding the world around us. they provide ways of gaining new insi

10、ghts 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 applie

11、d 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.this course will mainly introduce probability basic concepts and statistics basic methods to st

12、udents, 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, hypothes

13、is testing, and so on.1.1 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

14、 drawing conclusions based on information contained on the data. a population（總體）（總體） 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 p

15、roduced during a specified period. (2) all individuals who received a b.s. in engineering. (3) all students whos mathematics score above 70. sample（樣本）（樣本） 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 bulbssam

16、ple = 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

17、shipment?populationsample 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 informatio

18、n for some companies, taken from the stock investor pro panyexchangeticker symbolannual salesshare priceprice/earnings ratioaward softwraeotcawrd15.711.50022.5chesapeake energynysechk255.37.88012.7craig corporationnysecrg29.417.0007.5edistoamexedt254.69.6886.0elements, variables , and observations t

19、he 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 a

20、utomobile under specified conditions a univariate（單變）data set consists of observations on a single variable bivariate（雙變）data means observations are made on each of two variables. the set of measurements collected for a particular element is called an observation（觀察值）. branches of statisticsdescript

21、ive statistics（描述性統(tǒng)計(jì)）（描述性統(tǒng)計(jì)） 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（直方圖）, boxplots（箱線圖）, and

22、 scatter plots（散點(diǎn)圖）are primary examples. other descriptive methods involve calculation of numerical summary measures, such as means, standard deviations, and correlations coefficients.example 1.1 here is data consisting of observations on x = o-ring temperature for each test firing or a actual launc

23、h of the shuttle rocket engine2535455565758520103040 inferential statistics（推斷統(tǒng)計(jì)）（推斷統(tǒng)計(jì)）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 （統(tǒng)計(jì)推斷

24、）.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.example 1.2 material strength investigations provide a rich area of application for statistical methods. suppose we ha

25、ve 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

26、degree of confidence, the population mean strength is between 7.48 mpa and 8.80 mpa; we call this a confidence interval（置信區(qū)間）or interval estimate（區(qū)間估計(jì)）. 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 summarize