The course consists of 11 units, organised into two blocks: the first block, corresponding to Units 1 through 5, focuses on the study of probability. The second block, which includes Units from 6 through 11, takes account of the main tools of inferential statistics, with particular attention to confidence intervals and statistical hypothesis testing.
Unit 1 .- Uncertainty and probability.
1.1 .- Probability. Concepts and quantification.
1.2 . Axiomatic definition of probability.
1.3 .- Conditional probability and independence.
1.4 .- Total Probability and Bayes theorem.
Unit 2 .- Random variables.
2.1 .- Random variable. Discrete and continuous variables.
2.2 .- Probability distribution of a random variable.
2.3 .- Characteristics of random variables. Expected value and dispersion.
2.4 .- Chebyshev Inequality.
Unit 3 .- Discrete probability models.
3.1 .- Bernoulli processes and related distributions.
3.1.1- Binomial model.
3.1.2- Geometric model.
3.2 .- Hypergeometric Model.
3.3 .- Poisson model.
Unit 4 .- Continuous probability models.
4.1 .- Uniform model.
4.2 .- Normal model.
4.3 .- Other models.
Unit 5 .- Joint analysis and limit theorems.
5.1 .- K-dimensional distributions.
5.2 .- Independent random variables. Properties.
5.3 .- Aggregates of random variables.
5.4 .- Central Limit Theorem and its applications.
Unit 6 .- Introduction to sampling. Estimators.
6.1 .- Sample surveys. Sample selection techniques.
6.2 .- Simple random sampling. Distribution of the sample.
6.3 .- Estimators and their properties.
6.4 .- Methods of obtaining estimators.
Unit 7 .- Inferential tools. Distributions associated with sampling.
7.1 .- Distributions associated with the sampling process.
7.2 .- Inferential processes and relevant distributions.
Unit 8 .- Interval estimation.
8.1 .- Introduction to interval estimation.
8.2 .- Confidence intervals. Construction and characteristics.
8.3 .- Confidence intervals for the mean.
8.4 .- Confidence intervals for the proportion.
8.6 .- Confidence intervals for the variance.
Unit 9 .- Introduction to hypothesis testing.
9.1 .- Basics of statistical hypothesis testing.
9.2 .- Types of errors in hypothesis testing.
9.3 .- Methodology and implementation of statistical tests.
Unit 10 .- Parametric tests.
10.1 .- Tests for the mean.
10.2 .- Tests for the proportion.
10.3 .- Tests for the variance.
Unit 11 .- Non-parametric tests.
11.1- Runs test.
11.2 .- Normality testing.
11.3 .- Independence testing.