# PROBABILITY AND STATISTICS S CHAND PDF

damentals of probability and statistics using mostly calculus. I have given . For an event A of a discrete sample space S, the probability of A can be computed. You may go to the website Library Genesis and search for the book. If not found, search by the name of the book. You will find a list of books relevant to the topic. Fundamentals of Mathematical Statistics By S.C. Gupta – PDF Free Download Publisher: Sultan Chand & Sons; Language: English; ISBN

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PDF | Linear correlation coefficient Linear regression; Non-linear Text Book: Probability and Statistics By T K V Iyengar S chand, 3 rd Edition. PROBABILITY AND STATISTICS: (FOR 2ND YEAR cittadelmonte.info STUDENTS OF JNTU, ANANTAPUR). Dr. T K V Iyengar, Dr. M.V.S.S.N. PRASAD, S. Aim: To acquire basic knowledge in concepts of probability and statistics. Objective: The Edition, Sultan Chand & Sons educational Publishers. 2. Dr. B.S.

Contains, besides complete theory, more than fully solved examples and more than 1, thought-provoking Problems with Answers, and Objective Type Questions. V, , The book has been revised keeping in mind the comments and suggestions received from the readers. The book originally written twenty-four years ago has, during the intervening period, been revised and reprinted seve'ral times. They now take great pleilsure in presenting to the readers the ninth completely revised and enlarged edition of the book. The subjectmatter in the whole book has been rewritten in the light of numerous criticisms and suggestions received from the users of the previous editions in-lndia and abroad.

Hibbeler Book April Punmia, Ashok Kumar Jain, Arun April 8. April 7. Popular Files. January June 2. February 6. June Trending on EasyEngineering. Chopra Book Free Download November 1. An Introduction By Hamdy A. Taha Book Free February February 5. Verma Book Free Download February Gere, Stephen P. March 1. Never Miss. Methods Bowley himselr d. According to Boddington.. Introduction Statistics as 'Statistical Data' Webster defines Statistics ali "classified facts represt.

J'he third. But none of the above definitions is adequate.. Horace Secrist as follows: Some other definitions are: The first because1tatisticsJis not merely confined to the collection of data as other aspects like presentation.

Statistics may be defined as " the science which deals w th. In modern times. As such most of the large industrial and commercial enterprises are employing trailled and efficient statisticians. In the modem age which is termed as 'the age of planning'.

## TEXT BOOKS 1 TKV Iyengar B Krishna Gandhi and Others Probability and Statistics

Business executives are relying more and more on statistical techniques for studying the needs and the desires of the consumers and for many other purposes.

As such it is not confined to the affairs of the State but is intruding constantly into various diversified spheres of life. Wrong expectations.. Before starting with the production process he must have an. It has also facilitated the development of economic theory. Statistics is an indispensable tool of production control also. It is hardly possible to enumerate even a single department of human activity where statistics does not creep in.

Statistics and Industry. Statistics and Bl!. Suppose a businessman wants to manu facture readymade gannents. The success of a businessman more or less depends upon the accuracy and precision of his statistical forecasting.

Statistics is very widely used in 'Quality Control'. It has rather become indispensable in all phases of human endeavour. Statistics is indispensable to planning. It is now finding wide applications in almost all sciences. In order that planning is successful. Thus the fonnulation of a production plan in advance is a must which cannot be done without having q4alltitative facts about the details mentioned above. Statistics is viewed not as a mere device for collecting numerical data but as a means of developing sound techniques for their handl!

Importance and Scope of Statistics. Statistics and Psychology and Education. Statistics has found wide applications. Main contributors to statistics.

In medical science also. Statistics and War. Statistics and mathematics arc very intimately related. According to Connor.

The association between statistical methods and biological theories was first studied by Francis Galton in his work in 'Regressior: According to Prof. Bowley has rightJy said. The following are some of its important limitations: Karl Pearson.

Statistics may be regarded as that branch of mathematics which provided us with systematic methods of analysing a large I umber of related numerical facts. Statistics and Biology. Limitations of StatistiCs. In war. He says. Astronomy and Medical Science. In education and psychology. By the statement 'lje mean that as number of operations becomes larger and larger we should expect.

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.

Unlike the laws of physical and natural sciences. On the basis of statistical analysis we can tallc only in tenns of probability and chance and not in terms of certainty. Statistics is one of those sciences whose adepts must exercise the self-restraint of an artist. As the saying goes. Statistics deals with an aggregate of objects and does not give any specific recognition to the individual items of a series.

As such.

## Fundamentals of Mathematical Statistics [PDF] By S.C. Gupta Book PDF Free Download

As King says. For example. Individual items. 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. Statistical conclusicns are not universally true. Distrust of Statistics. When the skilled talkers. The facts supported by figures are psychologically more appealing. Accord'ing to Bowley. WlYoften hear the following interesting comments on Statistics: 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. Hence it is safer to walk in the middle of the road. Some of the reasons for the existence of such divergent views regarding the nature and function of Statistics are as follows: Liars figure'. As King points out. Hence drinking s harmful for longevity of life.

TABLE 1: A much better representation is given on the next page. This technique faciliiates the counting of the tally marks at the end. Having occurred four times. Frequency Distributions. But this does not reduce the bulk of the data.

When observations. A bar I called tally mark is put against the'number when it occurs. A better way may be to express the figures in an ascending or descending order of magnitude. The word 'frequency' is derived from 'how frequently' a variable occurs. QfonnatiQn is taken is not relevant.. TABLE 3 ': Marks are called the variable x and the 'number of students' against the marks is known as the frequency f of the variable.

This representation. Such a table showing the distribu. FQr example. It should preferably lie between 5 and CIauLimits 1. If this is not the case then the classification gives a distorted picCUre of the characteristics of the dala.

Jf possible. In spite of great importance of classification in statistical analysis. The ratios thus obtained are called 'frequency densities'. If the classes are of var: Comparable figures can be obtained by dividing the value of the frequencieS by the 'corresponding widths of the class intervals. The principle. Broad class intervals i.

Let us consider the distribution of age in years. Continuous Frequency Distribution. For practical purpose we re-writethe above clasSes as This form of frequency distribution is known as continuousj: It is often useful to represent a frequency distribution by means of a diagram which makes the unwieldy data intelligible and conveys to the eye the general run of the observations. Diagrammatic representation also facilitates the cOmparison of two or more frequency distributions.

We consider below some important types of graphic representation. It should be clearly understood that in. Age in years Below 5 5 or more but less than 10 10 or more but less than 15 15 or more but less than 20 20 or more but less than 25 and soon.

If class intervals are If we deal with a continuous variable. In such a case we form the class intervals as shown below. Frequency Polygon. For an ungrouped distribution. If the grouped' frequency distribution is not continuous. For a gtVuped frequency distribution. If the class intervals are of small width the polygon can be approximated by a smooth curve.

If d is the gap between the upper limit of any class and the lower limit of the Succeeding class Although the height of each rectangle is proportional to the frequency of the corresponding class. The upper and lower class limits of the new aclusive type classes are known as class boundaries. Since the grouped frequency distribution is not continuous. Arithmetic Mean Arithmetic mean of a set of observastions is their sum divided by the number of observations.

X is taken as the mid. According to Professor Bowley. Plainly speaking.. The symbol 1: The following are the five measures of central tendency that are in common use: By this we mean that if we are given the averages and sizes of a nwnber of series. Fundamentals Of Mllthem.. Requisites lor'an Ideal Measure ol'Central Tendency. In addition to t. At Summing both sides over i from 1 to n.

The arithmetic is reduced to a great extent. XIJi A. In case of grouped. Any number can serve the purpose of arbitrary point 'A' but. Algebraic suw of the deviations of a set of values from their arithmetic mean is zero. In this case. Calculate the meanfor thehllowingfrequency distribution. Properties or Arithmetic Mean Property If Xi It. Let XI I. X being the mean of distribution. Mean of the composite series. I'roperty 3.

This establishes the result. Applying the principle. I Ii Xi -'. If Xi. For the frequency distribution Xi IIi. Xi - Proof. Find tile percentage of male.. Merits and Demerits of Arithmetic.!.. We are giv. Mean Merits. Let X denote the avarage salary of all the workers in the firm.. Tile average salary of male employees in a fum was Rs.. But in practice this may not be so. If we are given the average marks alone we conclude that the level of intelligence of both the students at the end of the year is same.

Yule for an ideal average. Weighted Mean.

In case of extreme items. If some items in a distribution are more important than others. In calculating arithmetic' mean we suppose that all the items in the distribution have equal importance.

Ilarks obtained by two students A and B in three tests.. In such cases median discussed later is the only average to be used. Marks in: This is a fallacious conclusion since we find from the data that student A has improved consistently while student B has deteriorated consistently. If the weights attached to larger items are smaller and those attached to smaller items arc larger. Weighted mean gives the result equal to the simple mean if the weights assigned to each of the variate values arc equal..

It results in higher value than the simple mean if snuiller weights arc given to smaller items and larger weights to larger items. Let IV. Then we define: It may be observed that the formula for weighted mean is the same as tlie I'ormula for simple mean with f.

The first natural numbers arc I. In such cases.. In case of even number of observations. Median of Ii 4fstribution is the value of the variable which divides it into two equal pans.

In case of discrete frequency distribution median is obtained by considering the cumulative freqoencies. In case of ungrouped data. FI Fl If we are given a frequency.. I which is the required fonnula. Class interval: The class x. The cumulaltive frequency distribution is givC? Let us consider the following continuous frequency distribution. What is the median wage? Thus median class is Wages in Rs. Find the median wage of the following distribution: In afactory employing 3.

The' given infonnation can be expressed in tabular fonn as follows. Using the median formula. This property is sometimes described and. JIlate it by taking the mean of two middle terms. In some cases it can be located merely by inspection. For e. Here we shall locate mode by the method of grouping as explained below: The frequencies in column i are the original frequencies.

In all the above cases. Find the mode of the following frequency distribution: Size oX: Column ii is obtained by combining the frequencies two by two. Thtis in the case of discrete frequency distribution mode is the value oh corresponding 10 maximum frequency. But in anyone or-more of the following cases: Iq other words.

Mode is the value which occurs most frequently in a set of observastions and around which the otller items of the set clustez densely. If we leave the fust freqUency and combine the remaining frequencies two by two we get column iii. In case of continuous frequency distribution.. To fmd mode we form the following table: The mode is the value of x for which the frequency curve has a maxima Let the modal point be Q.

If It is the maximum of all the frequencies. X2-X" Frequency: Let us consider the continuous frequency disttibution: Or LM PD.. Here maximum frequency is Thus the class is the modal class. For a symmetrical distribution. In such cases If the method of grouping gives the modal class which does not correspood to the maximum frequency. Sometimes mode is estimated from the mean and the median. Using mode formula we get: If the distribution is moderately asymmetrical.

In case of irregularities in the distribution. Such distributions are called bi-modal. Merits and Demerits or Mode Merits.. It is not always possible to find a clearly defined mode Geometric Mean. G is given by 'G. If a distribution has more than two modes.. Like median. In SOlD" cases. Mode is the average to be used to find the ideal size. Xt"t tI". Merits and Demerits of Geometric Mean Merits U It is based upon all the-observations.

If nt and n2 are the sizes.. X is taken to be the value corresponding to the mid-point of the class-intervals. N i-I. C-eometric mean is used To fiild 'the rate of populati6il growth and the rate Of interest. Then their arithmetic mean C is given by: Hence in finding the arithmetic mean of a set of n readings on a thermometer. Show that in finding the arithmetic mean of a set of readings on thermometer it doe.

Centrigrade or Fahrenheit is important. Cn SC. Geometric mean G. A cyclist pedals from Iris. It gives greater importance to small items and is useful only when small items have to be given a greater weightage.

V Proof is left as an exercise to the reader. Merits and Demerits of Harmonic Mean Merits. Like geometric mean In going from house to college. If equal distances are covered travelled per unit of time wjth speeds equal to V. Hannonic mean is rigidly defined. Harmonic Mean Instead of tixed comtant distance being with varying speed. Total 15 1: Weighted Harmonic Mean.

Since different distances are covered with varying speeds. Speee' km. Distance inkm. These arc tbe values wbicb divide tbe series into a numocr of equal parts.

In that case. Since arithmetic mean satisfies all tbe properties of an ideal average as laid -down by Prof. YOII can take a trip which entails travelling km.. Wllat is YOt" average speed for tire entire distance? Selection of an Average. Partition Values. Calculate median. Hence Graphical Location of the Partition Values. First fonn the cumulative frequency table. Cumulative frequency cf. The third quartile. Eight coins were tossed together and the number f: The methods of computing the partition values are the same as those of locating the median in the case of both discrete and continuous distributions.

Take the class intervals or the variate values along the x-axis and plot the corresponding cumulative freqIJencies aJong the y-axis against the upper limit of the class inrerval or against the variare value in the case of discrete frequency distribution.

The farst quartile. The second quartile. The partition values. Hence D. The curve obtained on joining. The farst.. Marks-group ' No.

The graphicallucation of partition values from. Draw the cumulative frequency curve for the follOWing distribution showing the number of marks of59 students in Statistics.. Marks-group No. The smooth curve obtained on joining these points is called ogive or more particularly 'less than' ogive..

The median can also be located as follows: From the point of intersection of 'less than' ogive and 'more than' ogive. What are the principles governing the choice o: From 'A' draw a line p.

The abscissa of the point so obt. To locate the values of QI or Q3. Other partition values. Jing toNI4 or3NI4 and proceedexacdy similarly.

Examine these properties with reference to the Arithmetic Mean. Write short notes on: What are their uses? Critically examine both the averages.

Then abscissa of 'M' gives the value of median. In the above example.. The median is also an average. It satisfies 8Imost all the requirements of a good average. What are the requisites of a statisfactory average?

In this light compare the relative merits and demerits of three well-mown averages. Je consists of 34 observations recorded correct to the nearest integer. The following numbers give the weights of 55 sbJdents of a class.

Show that i Sum of deviations about arithmetic mean is zero. Discuss their merits. Sum of absolute deviations aboGt median is'least iii Sum of the squares of deviations about arithmetic mean is least 8.

## Text books 1 tkv iyengar b krishna gandhi and others

Choosing appropriate class-intervals. Fmd out the following: Prepare a suitable frequency table. Compare and contrast the merits and demerits of them. Show that the geometric mean is capable of funher mathematical treatment. A sam. For the above weights. C were given the job of rmding the average of numbers. Calculate the average. Calculate the true mean value. He averaged all other nwnbers and then added one. A's method: Divide the sets into sets of each.

Are these 'methods correct? Monthly wages in Rs. Age in years: C's method: Each one did his own simplification. B's method: Divide the set into 2. Acquire Knowledge in a Tools and concepts of Micro Economics. Develop skills in providing solutions for a Managerial decisions of an organization. Develop effective communication in Business and Accounting transactions. Ascertain the profitability and soundness of the organization. UNIT — I: Demand Analysis: Determinants of demand — demand function - law of demand and its exceptions - elasticity of demand — types - measurement and significance of elasticity of demand - demand forecasting and methods of demand forecasting.

Isoquants and isocosts — input-output relationship - law of returns - internal and external economies of scale. Cost Concepts:

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