An Introduction to Statistics and Probability

Contents : Foreword. Preface. I. Statistics and its Origin : 1. Development of statistics : historical perspectives. 2. Defining statistics. 3. Characteristics of statistics. 4. Uses and importance of statistics. 5. Population and sample. 6. Sources of statistical data. 7. Distrust of statistics. 8. Computer and statistics. II. Summarizing Data : 1. Introduction. 2. Meaning of data. 3. Defining a variable. 4. Types of data. 5. Summarizing and presenting data. 6. Presenting data by percentages, proportions and ratios. 7. Presenting data by graphs and diagrams. III. Descriptive statistics I : central tendency : 1. Introduction. 2. Measures of central tendency. 3. The arithmetic mean. 4.Computing arithmetic mean for grouped data. 5. Shot-cut method of computing mean. 6. Weighted arithmetic mean. 7. Some useful properties of arithmetic mean. 8. The median. 9. Computing median for raw data. 10. Computing median for classified and grouped data. 11. Locating median graphically. 12. quartiles, deciles and percentiles. 13. The mode. 14. Locating mode graphically. 15. The Geometric mean. 16. The harmonic mean. 17. Comparing the averages. IV. Descriptive statistics II : dispersion : 1. Meaning of dispersion. 2. Measures of dispersion. 3. Absolute measures of dispersion. 4. Relative measures of dispersion. 5. Empirical relations among measures of dispersion. 6. Comparing the measures of despersion. 7. A few more theorems on dispersion. 8. The moments. 9. Central moments in terms of raw moments. 10. Effect of changes in origin and scale on moments. 11. Shepard’s correction for moments. 12. Shape characteristics of a distribution. 13. Box and whiskers plot. 14. More theorems and examples. V. Simple regression and correlation : 1. Regression analysis : an introduction. 2. Regression model. 3. Population regression line. 4. Types of regression analysis. 5. Scatter diagram. 6. The least-squares method. 7. properties of regression coefficient. 8. Goodness of fit in regression. 9. Coefficient of determination. 10. Correlation analysis : an introduction. 11. Simple correlation coefficient. 12. Rank correlation. 13. Theorems and examples on correlation and regression. 14. More examples on correlation and regression. 15. Pearson’s from bivariate frequency table. 16. Correlation ratio. 17. Some special types of correlation coefficients. VI. Multiple regression analysis : 1. Introduction. 2. Estimating the parameters in the regression model. 3. Problems in interpreting the constants. 4. Multiple correlation coefficient. 5. Partial correlation coefficient. 6. Polynomial regression. VII. Probability : 1. Understanding probability. 2. Evolution of probability. 3. Set and set operations. 4. Operations with sets. 5. The algebra of sets. 6. Random phenomena and related concepts. 7. Counting rules. 8. Assigning probabilities to experimental outcomes. 9.The odds. 10. Theorems on probability. 11. Independence of events. 12. Non-independence of events. 13. Conditional probability. 14. Bayes’ theorem. 15. Miscellaneous examples. VIII. Random variables and its probability distribution : 1. Random variable. 2. Probability distribution. 3. Discrete probability distribution. 4. Discrete distribution function. 5. Continuous probability distribution. 6. Continuous distribution function. 7. Joint probability distribution. 8. Marginal distribution. 9. Conditional distribution. 10. Independence of random variable. 11. A few more examples. IX. Mathematical expectation : 1. Meaning of mathematical expectation. 2. Expected value of a function of a random variable. 3. Expected value of a function of two random variables. 4. Conditional expectation. 5. Conditional variance. 6. Moments and moment generating function. 7. Cumulants and cumulant generating function. 8. Relations between moments and cumulants. 9. Characteristic function. 10. Special mathematical expectation. X. Probability distributions : 1. Introduction. 2. Bernoulli distribution. 3. Binomial distribution. 4. Hypergeometric distribution. 5. Poisson distribution. 6. Negative binomial distribution. 7. Geometric distribution. 8. Multinomial distribution. 9. Uniform distribution-1. 10. Unifrom distribution-2. 11. Normal distribution. 12. Exponential distribution. 13. Gamma distribution. 14. Beta distribution. Bibliography. Appendix : 1. Binomial probability distributions. 2. Cumulative binomial distributions. 3. Values of e". 4. Poison probability distributions. 5. Cumulative poison distributions. 6. Cumulative normal distributions. Index.