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INTRODUCTION TO STATISTICS

 UNIT 1 INTRODUCTION TO STATISTICS Structure 1.0 Introduction 1.1 Objectives 1.2 Meaning of Statistics 1.2.1 Statistics in Singular Sense 1.2.2 Statistics in Plural Sense 1.2.3 Definition of Statistics 1.3 Types of Statistics 1.3.1 On the Basis of Function 1.3.2 On the Basis of Distribution of Data 1.4 Scope and Use of Statistics 1.5 Limitations of Statistics 1.6 Distrust and Misuse of Statistics 1.7 Let Us Sum Up 1.8 Unit End Questions 1.9 Glossary 1.10 Suggested Readings 1.0 INTRODUCTION The word statistics has different meaning to different persons. Knowledge of statistics is applicable in day to day life in different ways. In daily life it means general calculation of items, in railway statistics means the number of trains operating, number of passenger’s freight etc. and so on. Thus statistics is used by people to take decision about the problems on the basis of different type of quantitative and qualitative information available to them. However, in behavioural sciences, the ...
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GRAPHICAL METHODS IN OPERATION RESEARCH

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  Linear Programming Linear programming is a mathematical technique employed to determine the most favorable solution for a problem characterized by linear relationships. It is a valuable tool in fields such as operations research, economics, and engineering, where efficient resource allocation and optimization are critical. Now let’s learn about types of linear programming problems Types of Linear Programming Problems There are mainly three types of problems based on Linear programming they are, Manufacturing Problem:  In this type of problem, some constraints like manpower, output units/hour, and machine hours are given in the form of a linear equation. And we have to find an optimal solution to make a maximum profit or minimum cost. Diet Problem:  These problems are generally easy to understand and have fewer variables. Our main objective in this kind of problem is to minimize the cost of diet and to keep a minimum amount of every constituent in the diet.  Transpo...
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The connected components

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  3 The connected components   Molloy and Reed [1995] showed that for a random graph with vertices of degree i, where   are non-negative values which sum to 1, the giant component emerges when So long as the maximum degree is less than   They also show that almost surely there is no giant component when and maximum degree less than Here we compute Q for our graphs. We are thus led to consider the value   which is a solution to If We first summarize the results here: 1.    When   the random graph a. s. has no giant component. When   there is almost surely a unique giant component. 2.    When     almost surely the second largest components have size   there is almost surely a component of size x. 3.       When   almost surely the second largest components are of size For any   there is almost surely a component of size x. 4.      When   th...
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