Ebook Fundamentals of probability and statistics for engineers: Part 2
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Ebook Fundamentals of probability and statistics for engineers: Part 2
Part BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 1. we are concerned in this and subsequent chapters with step D —* E of the basic cycle in probabilistic modeling, that is. parameter estimation and model verification on the basis of observed data. In Chapters 6 and 7. our major concern has been the selection of an appropriate model (probability d Ebook Fundamentals of probability and statistics for engineers: Part 2 istribution) to represent a physical or natural phenomenon based on our understanding of its underlying properties. In order to specify the model compEbook Fundamentals of probability and statistics for engineers: Part 2
letely, however, it is required that the parameters in the distribution be assigned. We now consider this problem of parameter estimation using availaPart BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 ong a number of contending distributions when no single one is preferred on the basis of the underlying physical characteristics of a given phenomenon.Let us emphasize at the outset that, owing to (he probabilistic nature of the situation, the problem of parameter estimation is precisely that - an e Ebook Fundamentals of probability and statistics for engineers: Part 2 stimation problem. A sequence of observations, say 11 in number, is a sample of observed values of the underlying random variable. If we were to repeaEbook Fundamentals of probability and statistics for engineers: Part 2
l the sequence of n observations, the random nature of the experiment should produce a different sample of observed values. Any reasonable rule for exPart BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 ngle sequence of observations, finite in number, can be expected to yield true parameter values. What we are basically interested in, therefore, is to obtain relevant information about the distribution parameters by actually observing the underlying random phenomenon and using these observed numeric Ebook Fundamentals of probability and statistics for engineers: Part 2 al values in a systematic way.Fundamentals of Probability and Statistics for Engineers T.T. Soong © 2004 John Wiley & Sons. Lid ISBNs: 0-470-86813-9 (Ebook Fundamentals of probability and statistics for engineers: Part 2
H B) 0-470-86814-7 (PB)248Fundamentals of Probability and Statistics for Engineers8.1 HISTOGRAM AND FREQUENCY DIAGRAMSGiven a set of independent obserPart BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 luated. When there are a large number of observed data, a histogram is an excellent graphical representation of the data, facilitating (a ) an evaluation of adequacy of the assumed model, (b) estimation of percentiles of the distribution, and (c) estimation of the distribution parameters.Let us cons Ebook Fundamentals of probability and statistics for engineers: Part 2 ider, for example, a chemical process that is producing batches of a desired material: 200 observed values of the percentage yield. X. representing aEbook Fundamentals of probability and statistics for engineers: Part 2
relatively large sample size, arc given in Table 8.1 (Hill. 1975). The sample values vary from 64 to 76. Dividing this range into 12 equal intervals aPart BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 igure 8.1. A frequency diagram is obtained if the ordinate of the histogram is divided by the total number of observations. 200 in this case, and by the interval width d (which happens to be one in this example). We see that the histogram or the frequency diagram gives an immediate impression of the Ebook Fundamentals of probability and statistics for engineers: Part 2 range, relative frequency, and scatter associated with the observed data.In the case of a discrete random variable, the histogram and frequency diagrEbook Fundamentals of probability and statistics for engineers: Part 2
am as obtained from observed data take the shape of a bar chart as opposed to connected rectangles in the continuous case. Consider, for example, the Part BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Ebook Fundamentals of probability and statistics for engineers: Part 2 ercentage yield (data source: Hill, 1975)Observed Data and Graphical Representation249Table 8.1 Chemical yield data (data source: Hill. 1975)Batch no.Yield Batch no. (%)Yield Batch no. YieldBatch no.Yield (%)Batchno. Yield (%)(%)(%)168.44168.78168.512173.316170.5269.14269.18271.412275.816268.8371.04 Ebook Fundamentals of probability and statistics for engineers: Part 2 369.38368.912370.416372.9469.34469.48467.612469.016469.0572.94571.18572.212572.216568.1672.54669.48669.012669.816667.7771.14775.68769.412768.316767.18Ebook Fundamentals of probability and statistics for engineers: Part 2
68.64870.18873.012868.416868.1970.64969.08971.912970.016971.71070.95071.89070.713070.917069.01168.75170.19167.013172.617172.01269.55264.79271.113270.1Part BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in Chapter Part BStatistical Inference, ParameterEstimation, and Model Verification8Observed Data and Graphical RepresentationReferring to Figure 1.1 in ChapterGọi ngay
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