FIRST PART. PROBABILITY THEORY
Chapter 1. Statistical Science
1. Introduction
2. Basic concepts
3. Problems solved by Statistics
4. Historical background
Chapter 2. Introduction to probabilities
1. Concept of probability
2. Probability axioms
3. Basic properties
4. Conditional probability
5. Classification of events in a sample space
Chapter 3. Probability interpretations
1. Laplace interpretation
2. Frequentist interpretation
3. Logical interpretation
4. Subjective interpretation
Chapter 4. Fundaments of Bayesian Statistics
1. Prior and posterior probabilities
2. Likelihood function
3. Law of total probability
4. Bayes’ theorem
Chapter 5. Random variables
1. Concept of random variable
2. Probability distribution. Discrete and continuous random variables
3. Cumulative distribution function
4. Probability mass function
5. Probability density function
Chapter 6. Measures of a random variable
1. Measures of central tendency
2. Measures of dispersion
3. Typification of random variables
4. Chebyshev’s inequality
5. Measures of shape
Chapter 7. Discrete distributions
1. Dichotomous distribution
2. Binomial distribution
3. Poisson distribution
4. Multinomial distribution
Chapter 8. Continuous distributions
1. Uniform distribution
2. Normal distribution
3. Chi-squared distribution
4. Student’s t-distribution
Chapter 9. Convergence of random variables
1. Random variables succession and its convergence
2. Types of convergence
3. Laws of large numbers
4. Central limit theorem
SECOND PART. ESTIMATION THEORY
Chapter 10. Sampling theory
1. Introduction to statistical inference
2. Problems solved by statistical inference
3. Sampling basic concepts
4. Types of sampling
5. Simple random sample
Chapter 11. Sample statistics
1. Concept of statistic
2. Statistic sample mean
3. Statistic sample variance
Chapter 12. Distributions of statistics
1. Distribution of sample mean
2. Distribution of sample variance
3. Distribution of sample proportion
4. Distribution of difference between sample means
5. Distribution of difference between sample proportions
Chapter 13. Estimators
1. Concept ant types of estimation
2. Unbiased estimators
3. Efficient estimators
4. Consistent estimators
5. Sufficient estimators
6. Invariant estimators
7. Robust estimators
Chapter 14. Confidence intervals
1. Concept of confidence interval
2. Confidence interval for mean
3. Confidence interval for variance
4. Confidence interval for proportion
5. Confidence interval for difference between means
6. Confidence interval for difference between proportions
THIRD PART. STATISTICAL HYPOTHESIS TESTING
Chapter 15. Fundaments of statistical hypothesis testing
1. Introduction
2. Statistical hypothesis
3. Types of tests
4. Errors of the first and second kinds
5. Critical region and region of acceptance
Chapter 16. Parametric tests
1. Introduction
2. Neyman-Pearson tests
3. Significance tests
Chapter 17. Nonparametric tests
1. Introduction
2. Runs test for randomness hypothesis
3. Shapiro-Wilks test for normality of the population
4. Chi-square goodness-of-fit test
5. Kolmogorov-Smirnov goodness-of-fit test
FOURTH PART: MULTIVARIATE STATISTICS.
Chapter 18. Factor Analysis
1. Introduction
2. Adequacy of using Factor Analysis
3. Factor matrix
4. Number of factors and interpretation
5. Factor rotation
Exercises
Chapter 19. Cluster Analysis
1. Introduction
2. Types of data and similarity measures
3. Hierarchical clustering
4. Non-hierarchical clustering
Exercises
Chapter 20. Discriminant Analysis
1. Introduction
2. Bayes’ rule
3. Discriminant Analysis procedure
4. Misclassification error
Exercises
BIBLIOGRAPHY
1. Univariate Moments
2. Standard normal distribution tabulated
3. Chi-squared distribution tabulated
4. Student’s t-distribution tabulated
5. Values of lower and upper bounds of critical region in runs test
6. Coefficients of Shapiro-Wilk test
7. Critical values of Shapiro-Wilk test
8. Critical values of Kolmogorov-Smirnov test