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An Introduction to Statistics and Probability by Nurul Islam: A Review

Statistics and probability are two branches of mathematics that deal with data analysis, inference, modeling, and uncertainty. They are essential tools for many fields of science, engineering, business, and social sciences. However, learning statistics and probability can be challenging for many students, especially if they lack a solid background in mathematics.

One of the books that aims to help students overcome this difficulty is An Introduction to Statistics and Probability by Nurul Islam, a former professor of statistics at the University of Dhaka, Bangladesh. This book, which is now in its fourth revised edition, covers the basic concepts and methods of descriptive and inferential statistics, as well as probability theory. It also introduces some topics in regression analysis, multiple regression analysis, and random variables.

The book is written in a clear and concise style, with plenty of examples, exercises, and diagrams to illustrate the concepts. The book also uses real-world data sets from various fields to show the applications of statistics and probability. The book is suitable for undergraduate students who are taking introductory courses in statistics and probability, as well as for anyone who wants to learn the fundamentals of these subjects.

The book is divided into eight chapters, each with a summary and a set of review questions at the end. The chapters are as follows:

Chapter 1: Statistics and Its Origin. This chapter provides an overview of the history and development of statistics, its definition and characteristics, its uses and importance, its sources and types of data, its limitations and pitfalls, and its relation to computers.

Chapter 2: Summarizing Data. This chapter explains how to organize and present data using frequency distributions, graphs, and diagrams. It also discusses the level of measurement, the variable and attribute distinction, and the cumulative frequency distribution.

Chapter 3: Descriptive Statistics I: Central Tendency. This chapter introduces the measures of central tendency, such as the arithmetic mean, the median, the mode, the geometric mean, and the harmonic mean. It also compares their properties and advantages.

Chapter 4: Descriptive Statistics II: Dispersion. This chapter introduces the measures of dispersion, such as the range, the mean deviation, the variance, the standard deviation, the coefficient of variation, and the quartile deviation. It also discusses their properties and relations.

Chapter 5: Simple Regression and Correlation. This chapter introduces the concepts of regression analysis and correlation analysis. It explains how to fit a simple linear regression model using the least squares method, how to measure the strength of linear relationship using Pearson's correlation coefficient or Spearman's rank correlation coefficient, how to test the significance of regression and correlation parameters using t-test or F-test, how to partition the total variation using ANOVA table or coefficient of determination.

Chapter 6: Multiple Regression Analysis. This chapter extends the concepts of regression analysis to multiple regression analysis. It explains how to fit a multiple linear regression model using matrix notation or normal equations method,

how to measure the strength of multiple linear relationship using multiple correlation coefficient or partial correlation coefficient,

how to test the significance of multiple regression parameters using t-test or F-test,

how to partition the total variation using ANOVA table or coefficient of determination,

and how to deal with polynomial regression models.

Chapter 7: Probability: A Measure of Uncertainty. This chapter introduces the concepts of probability theory. It explains how to define probability using axioms or relative frequency approach,

how to use set theory and counting rules to calculate probabilities,

how to use joint probability, conditional probability,

and independence of events to analyze probabilities,

how to use Bayes' theorem to update probabilities based on new information,

and how to solve various problems involving probabilities.

Chapter 8: Random Variables and Its Distributions. This chapter introduces the concepts of random variables and probability distributions. It explains how to define discrete and continuous random variables,

how to calculate their expected values,

variances,

and moments,

how to use binomial distribution,

Poisson distribution,

normal distribution,

and other common distributions to model various phenomena,

and how to use standardization technique or normal approximation method to calculate probabilities involving random variables.

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