BLOCK 0: DESCRIPTIVE STATISTICS
0. Descriptive Statistics
BLOCK I: PROBABILITY
1. Introduction to Probability
1.1 Introduction
1.2 Random phenomena
1.3 Definition of probability and properties
1.4 Conditional probability
1.5 Bayes Theorem
2. Random variables
2.1 Definition of random variable
2.2 Discrete random variables
2.3 Continuous random variables
2.4 Characteristic features of a random variable
2.5 Transformations of random variables
2.6 Random vectors
3. Distribution models
3.1 Binomial distribution
3.2 Poisson distribution
3.3 Geometric distribution
3.4 Uniform distribution (continuous)
3.5 Exponential distribution
3.6 Normal distribution (with CLT)
BLOCK II: ESTIMATION AND INFERENCE
4. Parameter estimation
4.1 Introduction and basic concepts
4.2 Sampling distributions
4.3 Maximum Likelihood Estimation
4.4 Properties of Maximum Likelihood Estimators
4.5 Inference based on MLEs
5. Statistical Inference
5.1 Introduction
5.2 Confidence Intervals
5.3 Hypothesis testing
5.4 Particualr tests on a single sample
5.5 Comparison of two populations
5.6 Statistical quality control
BLOCK III: APPLICATIONS
6. Statistical quality control
6.1 Introduction to statistical process control
6.2 Variables charts, the Xbar chart
6.3 Attributes charts, p and np charts
7. Linear regression
7.1 Introduction
7.2 Simple linear regression
7.3 Multiple linear regression
7.4 Comparison of three or more population means (ANOVA)