Fundamentals of Statistics covers topics on the introduction, fundamentals, and science of statistics. The book discusses the collection, organization and. MASX Fundamentals of Statistics I. Lecture Notes. Professor S. G. Gilmour. School of Mathematical Sciences. Queen Mary, University of. Such stories as these would not be possible to understand without statistics, the fundamentals of statistics and introduce you to concepts that are used.
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These lecture notes have been used at Basics of Statistics course held in Uni- versity of Statistics is a very broad subject, with applications in a vast number of . In the fourth chapter, the fundamentals of descriptive statistics, the neces(sary basis for the data processed. The fifth chapter deals with the estimation of. FUNDAMENTAL OF MATHEMATICAL STATISTICS-S C GUPTA & V K KAPOOR. pdf - Ebook download as PDF File .pdf), Text File .txt) or read book online.
It is not inaccurate to say that randomness is present in any realistic conceptual model of a real-world phenomenon. As in other scientific modeling procedures, the basic cycle of this undertaking consists of a number of fundamental steps; these are schematically presented in Figure 1.
A basic understanding of probability theory and random variables is central to the whole modeling process as they provide the required mathematical machinery with which the modeling process is carried out and consequences deduced.
The step from B to C in Figure 1. Model verification and parameter estimation E on the basis of observed data D fall within the framework of statistical inference.
A model A: Probability and random variables B: Factual observations and nature of scientific phenomenon C: Construction of model structure D: Observed data E: Model verification and parameter estimation F: Model analysis and deduction Figure 1. A reexamination of factual observations or additional data may be required here. Finally, model analysis and deduction are made to yield desired answers upon model substantiation. In line with this outline of the basic steps, the book is divided into two parts.
Part A Chapters 2—7 addresses probability fundamentals involved in steps A! C, and E! F Figure 1. Chapters 2—5 provide these fundamentals, which constitute the foundation of all subsequent development.
Some important probability distributions are introduced in Chapters 6 and 7. The nature and applications of these distributions are discussed. An understanding of the situations in which these distributions arise enables us to choose an appropriate distribution, or model, for a scientific phenomenon. Part B Chapters 8—11 is concerned principally with step D!
FUNDAMENTAL OF MATHEMATICAL STATISTICS-S C GUPTA & V K KAPOOR.pdf
E Figure 1. Starting with data and data representation in Chapter 8, parameter estimation techniques are carefully developed in Chapter 9, followed by a detailed discussion in Chapter 10 of a number of selected statistical tests that are useful for the purpose of model verification. In Chapter 11, the tools developed in Chapters 9 and 10 for parameter estimation and model verification are applied to the study of linear regression models, a very useful class of models encountered in science and engineering.
The topics covered in Part B are somewhat selective, but much of the foundation in statistical inference is laid. This foundation should help the reader to pursue further studies in related and more advanced areas. To facilitate these calculations, some of the probability tables are provided in Appendix A.
It should be pointed out, however, that a large number of computer software packages and spreadsheets are now available that provide this information as well as perform a host of other statistical calculations.
The mathematical prerequisite for a course using this book is a good understanding of differential and integral calculus, including partial differentiation and multidimensional integrals.
Familiarity in linear algebra, vectors, and matrices is also required. In studying a random phenomenon, we are dealing with an experiment of which the outcome is not predictable in advance. Experiments of this type that immediately come to mind are those arising in games of chance. Kindly Note: Thank you for visiting my thread.
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Your Comments About This Post. Is our service is satisfied, Anything want to say? Cancel reply. Statistics, with its wide applications in almost every sphere of hUman ac!
The following are some of its important limitations: ie; Fundamentals of Mathematical Statistics i Statistics is not suitedto the study of qualitative phenomenon.
Statistics, being a science dealing with a set of numerical data, is applicable to the study of only those subjects of enquiry which are capable of quantitative measurement. As such; qualitative phenomena like honesty, poverty, culture, etc.
However, statistical techniques may be applied indirectly by first reducing the qualitative expressions to precise quantitative tenns. For example, the intelligenc. Statistics deals with an aggregate of objects and does not give any specific recognition to the individual items of a series.
Individual items, taken separately, do:not constitute statistical data and are meaningless for any statistical enquiry. Hence, statistical analysis is suitod to only those problems where group characteristics are to be studied iii Statistical laws are not eXilct.
Unlike the laws of physical and natural sciences, statistica1laws are only approximations and not exact. On the basis of statistical analysis we can tallc only in tenns of probability and chance and not in terms of certainty.
Statistical conclusicns are not universally true - they are true only on an average. It may happen that fifth man also dies of the operation or it may also happen that of the.
Perhaps the most important limitation of Statistics is that it must be uSed by experts. As the saying goes, " Statistical methods are the most dangerous tools in the hands of the inexperts.
Statistics is one of those sciences whose adepts must exercise the self-restraint of an artist. One of the greatest shoncomings of Statistics is that they do not bear on their face the'label of their quality and as such carl be moulded and manipulated in any manner to suppon one's way of argument and reasoning. As King says, " Statistics are like clay of which one can niake a god or devil as one pleases.
Introduction I '1 Distrust of Statistics. WlYoften hear the following interesting comments on Statistics: i 'AI ounce of truth will produce tons of Statistics', ii 'Statistics can prove anything', iii 'Figures do not lie. Liars figure', iv 'If figures say so it can't be otherwise', v 'There are three type of lies - lies, demand lies, and Statistics - wicked in the order ofotheirnaming, and so on.
Some of the reasons for the existence of such divergent views regarding the nature and function of Statistics are as follows: i Figures are innocent, easily believable and more convincing. The facts supported by figures are psychologically more appealing. When the skilled talkers. It may be pointed out that Statistics neither proves anything nor disproves anything. It is only a tool which if rightly used may prove extremely useful and if misused. Accord'ing to Bowley.
As King points out. Hence it is safer to walk in the middle of the road. Thus, Mathematics is gaining 'popularity among the students of the university. Hence drinking s harmful for longevity of life. Frequency Distributions.
A better way may be to express the figures in an ascending or descending order of magnitude, commonly termed as array. But this does not reduce the bulk of the data.
A much better representation is given on the next page. A bar I called tally mark is put against the'number when it occurs. Having occurred four times.
This technique faciliiates the counting of the tally marks at the end. Marks are called the variable x and the 'number of students' against the marks is known as the frequency f of the variable. The word 'frequency' is derived from 'how frequently' a variable occurs. For example, in the above case the frequency of 31 is 10 as there are ten students getting 31 marks.Using the median formula.
Here maximum frequency is WlYoften hear the following interesting comments on Statistics: i 'AI ounce of truth will produce tons of Statistics', ii 'Statistics can prove anything', iii 'Figures do not lie.
A reexamination of factual observations or additional data may be required here.
The followiflg data represent travel expenses other than transportation for 7 trips made during November by a salesman for a small fmn: Compare and contrast the merits and demerits of them. Liars figure', iv 'If figures say so it can't be otherwise', v 'There are three type of lies - lies, demand lies, and Statistics - wicked in the order ofotheirnaming, and so on.
Chapter 1 Fundamental Statistics.pdf - Engineering...
Frequency Distributions. Statistical conclusicns are not universally true. Due care has been taken of the examination r.
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