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Download Nurul Islam's Book on Statistics and Probability: A Clear, Concise, and Comprehensive Resource


Here is the outline of the article: # An Introduction to Statistics and Probability by Nurul Islam PDF Free Download ## Introduction - What is statistics and probability? - Why are they important for students and researchers? - What are the main topics covered in this book? - How can you download this book for free? ## Statistics and Its Origin - Statistics: its origin and development - General field of statistics - Defining statistics - Characteristics of statistics - Uses and importance of statistics - Population and sample - Sources of statistical data - Distrust in statistics - Computer and statistics ## Summarizing Data - Meaning of data - Level of measurement - Variable and attribute - Summarizing and presenting data - Frequency distribution - Other forms of frequency distribution - Desirable features of a frequency table - Presenting data by graphs and diagrams ## Descriptive Statistics I: Central Tendency - Measures of central tendency - The arithmetic mean - The median - Quartiles, percentiles and deciles - The mode - The geometric mean - The harmonic mean - Other measures of average - Comparing the averages ## Descriptive Statistics II: Dispersion - Meaning of dispersion - Measures of dispersion - Absolute measures of dispersion - Relative measures of dispersion - Empirical relations among measures of dispersion - Comparing the measures of dispersions - The moments - Shape characteristics of a distribution - Box and whisker plots ## Simple Regression and Correlation - Regression analysis: an introduction - Simple linear regression model - Types of regression analysis - Scatter diagram - The least squares method - Properties of regression coefficient - Partitioning the total variation in regression - Goodness of fit in regression - Correlation analysis - Measuring the correlation - Rank correlation ## Multiple Regression Analysis - Multiple regression model - Estimating the parameters in the model - Some properties of the estimators - Partitioning the total sum of squares - Problems in interpreting the constants - Multiple correlation - Partial correlation - Polynomial regression ## Probability: A Measure of Uncertainty - Understanding probability - Probability: historical perspectives - A review of set and set notations - Operations with sets - Law of sets - Random phenomenon and related concepts - Counting rules: permutation and combination - Assigning probabilities to experimental outcomes - The odds - Joint probability - Conditional probability - Independence of events - Selected theorems on probability - Bayes theorem ## Random Variables and Its Distributions - Random variables: discrete and continuous - Probability distribution function (PDF) - Cumulative distribution function (CDF) - Expected value or mean value - Variance and standard deviation - Moment generating function (MGF) - Some discrete probability distributions: binomial, Poisson, geometric, negative binomial, hypergeometric - Some continuous probability distributions: uniform, normal, exponential, gamma ## Sampling Distributions and Estimation - Sampling distributions: an introduction - Sampling distribution of sample mean - Sampling distribution of sample proportion - Sampling distribution of sample variance - Central limit theorem - Point estimation - Properties of point estimators - Methods of point estimation - Interval estimation - Confidence interval for population mean - Confidence interval for population proportion - Confidence interval for population variance ## Hypothesis Testing - Hypothesis testing: an introduction - Null and alternative hypotheses - Type I and type II errors - Level of significance and power of a test - One-tailed and two-tailed tests - Test statistic and p-value - Hypothesis testing for population mean - Hypothesis testing for population proportion - Hypothesis testing for population variance ## Analysis of Variance (ANOVA) - ANOVA: an introduction - One-way ANOVA - Assumptions of ANOVA - ANOVA table and F-test - Multiple comparisons - Two-way ANOVA - Interaction effects ## Chi-Square Test and Contingency Table Analysis - Chi-square test: an introduction - Chi-square test for goodness of fit - Chi-square test for independence - Contingency table analysis - Measures of association ## Nonparametric Statistics - Nonparametric statistics: an introduction - Advantages and disadvantages of nonparametric statistics - Some common nonparametric tests: sign test, Wilcoxon signed rank test, Mann-Whitney U test, Kruskal-Wallis test, Friedman test, Spearman rank correlation ## Conclusion - Summary of the main points of the article - Benefits of reading this book - How to download this book for free - Call to action ## FAQs - What is the difference between statistics and probability? - Who is the author of this book and what are his credentials? - What are the prerequisites for reading this book? - How can I access the solutions manual for this book? - Where can I find more resources on statistics and probability? Here is the article: # An Introduction to Statistics and Probability by Nurul Islam PDF Free Download ## Introduction Statistics and probability are two branches of mathematics that deal with data analysis, inference, modeling, and decision making. Statistics is the science of collecting, organizing, summarizing, and interpreting data to draw conclusions or make predictions. Probability is the study of the likelihood or chance of events occurring in various situations. Statistics and probability are important for students and researchers in many fields, such as natural sciences, social sciences, engineering, business, medicine, education, and more. They help us to understand the patterns, trends, relationships, and uncertainties in data. They also help us to design experiments, surveys, tests, and other methods of data collection. They enable us to make informed decisions based on evidence and logic. One of the best books to learn statistics and probability is An Introduction to Statistics and Probability by Nurul Islam. This book covers the basic concepts and methods of statistics and probability in a clear, concise, and comprehensive way. It also provides many examples, exercises, tables, graphs, and diagrams to illustrate the topics. It is suitable for undergraduate students as well as anyone who wants to learn or review statistics and probability. If you are interested in reading this book, you might be wondering how you can download it for free. Well, you are in luck because in this article we will show you how you can get a PDF copy of this book without paying anything. But before we do that, let us first take a look at what this book has to offer. ## Statistics and Its Origin In this chapter, you will learn about the history and development of statistics as a discipline. You will also learn about the general field of statistics and its branches. You will learn how to define statistics and what are its characteristics. You will also learn about the uses and importance of statistics in various fields of study and application. You will learn about the concepts of population and sample, which are essential for statistical inference. You will also learn about the sources of statistical data and how they can be classified into primary and secondary data. You will also learn about some common reasons why people distrust statistics and how to overcome them. Finally, you will learn about the role of computer in statistics and how it has revolutionized the field. ## Summarizing Data In this chapter, you will learn how to summarize and present data in a meaningful way. You will learn what data is and how it can be measured at different levels: nominal, ordinal, interval, or ratio. You will also learn about the difference between variable and attribute, which are two types of data. You will learn how to summarize data using frequency distribution, which is a table that shows how often each value or category occurs in a data set. You will also learn how to construct frequency distribution for discrete or continuous data using different methods. You will also learn about other forms of frequency distribution such as relative frequency distribution, percentage frequency distribution, cumulative frequency distribution, etc. You will also learn about the desirable features of a frequency table such as class intervals, class boundaries, class marks, class width, etc. learn how to present data by graphs and diagrams, which are visual representations of data. You will learn about different types of graphs and diagrams such as bar chart, pie chart, histogram, frequency polygon, ogive, stem-and-leaf plot, etc. You will also learn how to choose the appropriate graph or diagram for different types of data and how to interpret them. You will also learn how to use computer software such as Excel or SPSS to summarize and present data. ## Descriptive Statistics I: Central Tendency In this chapter, you will learn how to describe the center or typical value of a data set using measures of central tendency. You will learn about different measures of central tendency such as arithmetic mean, median, quartiles, percentiles, deciles, mode, geometric mean, harmonic mean, etc. You will also learn how to calculate these measures for different types of data using formulas or computer software. You will also learn about the properties and advantages and disadvantages of these measures. You will also learn how to compare the averages of two or more data sets using graphical or numerical methods. ## Descriptive Statistics II: Dispersion In this chapter, you will learn how to describe the spread or variability of a data set using measures of dispersion. You will learn about different measures of dispersion such as range, interquartile range, mean deviation, variance, standard deviation, coefficient of variation, etc. You will also learn how to calculate these measures for different types of data using formulas or computer software. You will also learn about the properties and advantages and disadvantages of these measures. You will also learn how to compare the dispersions of two or more data sets using graphical or numerical methods. You will also learn about some empirical relations among measures of dispersion such as Chebyshev's theorem and empirical rule. You will also learn about the moments of a distribution, which are numerical values that describe the shape and characteristics of a distribution. You will learn about different types of moments such as raw moments, central moments, standardized moments, etc. You will also learn how to calculate these moments for different types of data using formulas or computer software. You will also learn about the effects of changes in origin and scale on moments and how to correct them using Sheppard's correction. You will also learn about the shape characteristics of a distribution such as skewness and kurtosis. Skewness is a measure of the asymmetry or lack of symmetry of a distribution. Kurtosis is a measure of the peakedness or flatness of a distribution. You will learn how to measure skewness and kurtosis using formulas or computer software. You will also learn how to interpret these measures and what they imply about the distribution. You will also learn about box and whisker plots, which are graphical displays that summarize the five-number summary of a data set: minimum value, first quartile, median, third quartile, and maximum value. You will learn how to construct box and whisker plots for different types of data using computer software. You will also learn how to interpret box and whisker plots and what they reveal about the center, spread, and shape of a distribution. ## Simple Regression and Correlation In this chapter, you will learn how to study the relationship between two variables using regression and correlation analysis. Regression analysis is a method of finding the best-fitting line or curve that describes the relationship between two variables: one dependent variable (or response variable) and one independent variable (or explanatory variable). Correlation analysis is a method of measuring the strength and direction of the linear relationship between two variables. of regression analysis such as simple nonlinear regression, multiple regression, etc. You will also learn how to draw a scatter diagram, which is a graphical display that shows the relationship between two variables using dots or points. You will also learn how to use the least squares method, which is a method of finding the best-fitting line or curve that minimizes the sum of squared errors or residuals. You will also learn about the properties of regression coefficient, which is a measure of the slope or steepness of the regression line or curve. You will also learn how to partition the total variation in regression into explained variation and unexplained variation. You will also learn how to measure the goodness of fit in regression using coefficient of determination or R-squared, which is a measure of how well the regression line or curve fits the data. You will also learn about correlation analysis and how to measure the correlation between two variables using different methods such as Pearson's product-moment correlation coefficient or r, which is a measure of the strength and direction of the linear relationship between two variables. You will also learn about rank correlation, which is a measure of the strength and direction of the monotonic relationship between two variables based on their ranks or orders. You will also learn about some useful results and formulas related to correlation and regression such as properties of correlation coefficient, relation between correlation and regression coefficient, standard error of estimate, etc. You will also learn how to calculate Pearson's r from bivariate frequency table and how to measure correlation ratio, which is a measure of the strength of the nonlinear relationship between two variables. You will also learn about some further aspects of correlation such as partial correlation, multiple correlation, spurious correlation, etc. ## Multiple Regression Analysis In this chapter, you will learn how to study the relationship between one dependent variable and two or more independent variables using multiple regression analysis. Multiple regression analysis is a generalization of simple linear regression analysis that allows for more than one independent variable. You will learn about multiple regression model, which is a model that assumes a linear relationship between one dependent variable and two or more independent variables. You will also learn how to estimate the parameters in the model using different methods such as ordinary least squares method, which is a method of finding the best-fitting plane or hyperplane that minimizes the sum of squared errors or residuals. You will also learn about some properties of the estimators such as unbiasedness, consistency, efficiency, etc. You will also learn how to partition the total sum of squares into regression sum of squares and error sum of squares. You will also learn about some problems in interpreting the constants such as multicollinearity, heteroscedasticity, autocorrelation, etc. You will also learn about multiple correlation, which is a measure of how well the multiple regression model fits the data. You will also learn about partial correlation, which is a measure of how well one independent variable explains the dependent variable after controlling for other independent variables. You will also learn about polynomial regression, which is a type of nonlinear regression that assumes a polynomial relationship between one dependent variable and one independent variable. ## Probability: A Measure of Uncertainty subjective probability, etc. You will also learn about some basic concepts and notations related to probability such as experiment, outcome, sample space, event, etc. You will also learn how to use set theory and set operations to deal with events and probabilities. You will also learn about some laws of sets such as commutative law, associative law, distributive law, De Morgan's law, etc. You will also learn about random phenomenon and related concepts such as equally likely outcomes, mutually exclusive events, exhaustive events, complementary events, etc. You will also learn how to use counting rules such as permutation and combination to find the number of possible outcomes in an experiment. You will also learn how to assign probabilities to experimental outcomes using different methods such as classical method, relative frequency method, subjective method, etc. You will also learn about the odds of an event, which is a ratio that compares the probability of an event occurring to the probability of an event not occurring. You will also learn about joint probability, which is the probability of two or more events occurring together. You will also learn about conditional probability, which is the probability of one event occurring given that another event has occurred. You will also learn about independence of events, which is a condition that states that the occurrence of one event does not affect the occurrence of another event. You will also learn about some selected theorems on probability such as addition rule, multiplication rule, total probability rule, etc. You will also learn about Bayes' theorem, which is a formula that allows us to update our prior beliefs or probabilities based on new information or evidence. ## Random Variables and Its Distributions In this chapter, you will learn about random variables and its distributions. A random variable is a variable that takes on different values depending on the outcome of a random experiment. A distribution is a function that describes how the values of a random variable are distributed or spread out. You will learn about different types of random variables such as discrete and continuous random variables. A discrete random variable is a random variable that can take on only a finite or countable number of values. A continuous random variable is a random variable that can take on any value in an interval or range. You will also learn about probability distribution function (PDF), which is a function that gives the probability of each possible value of a discrete random variable or the probability density of each possible value of a continuous random variable. You will also learn about cumulative distribution function (CDF), which is a function that gives the probability of a random variable being less than or equal to a given value. You will also learn about expected value or mean value, which is a measure of the center or average value of a random variable. You will also learn about variance and standard deviation, which are measures of the spread or variability of a random variable. You will also learn about moment generating function (MGF), which is a function that generates all the moments of a random variable using derivatives. geometric distribution, negative binomial distribution, hypergeometric distribution, etc. These are distributions that describe the probability of certain types of discrete events such as number of successes in a fixed number of trials, number of occurrences of an event in a fixed interval of time or space, number of trials until the first success, number of failures until the rth success, number of successes in a sample drawn from a population, etc. You will learn how to identify these distributions and how to calculate their parameters, PDFs, CDFs, expected values, variances, and MGFs. You will also learn about some continuous probability distributions such as uniform distribution, normal distribution, exponential distribution, gamma distribution, etc. These are


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