Università Roma Tre

The Statistics course introduces students to the techniques of collecting, organizing, and analysing statistical data. The course also introduces students to the basic concepts of probability calculus and statistical inference for the analysis of statistical data derived from sample surveys.
All topics will also be illustrated using statistical software R through RStudio. The exercises and part of the lectures will be carried out in the computer room or remotely using the statistical software.
For each statistical methodology, a specific application will be illustrated on data sets on which students can practice. Therefore, the student will be taught not only to apply statistical techniques but also to choose the most appropriate technique and to comment on the output for decision-making purposes.
Exploratory Data Analysis
- Statistical characters and measurement scales. Simple distributions. Graphical display of data. Empirical distribution function.
-Position, variability and shape of statistical distributions.
- Double, marginal and conditional statistical distributions. Moments of double distributions, correlation.
Examples of exploratory data analysis using statistical software.
Elements of Probability Calculus
- Conditional probability. Independence. Bayes' rule. Discrete random variables. Probability function, density function, distribution function. Moments of random variables.
- Discrete probability distributions: binomial, Poisson, uniform.
- Continuous probability distributions: uniform, normal, Student's t, χ^2, exponential.
- Linear combinations of random variables, convergence, law of large numbers and central limit theorem.
- Use of statistical software to represent probability distributions and their properties.
Statistical Inference
- Population and sample: finite and infinite populations; random sample from finite and infinite populations; probability distribution of random sample.
- Sample statistics and their distributions.
- Parameter estimation: properties of estimators.
- Confidence intervals for a mean and a proportion.
- Hypothesis testing: elements of statistical tess, tests for means, proportions, and tests for difference in means and proportions.
- Hypothesis testing of independence and conformity.
- Simple linear regression estimation and hypothesis testing on the parameters of the regression line.
- Application of statistical methodologies through analysis of simple datasets using statistical software.

Newbold P. , Carlson W. & Thorne B. (2021) Statistics for Business and Economics, Pearson ed.

Other course material is available on Teams, Moodle and OneDrive.
Solutions to some exercises and exam assignments are also available at the website:
https://corsodistatistica.wixsite.com/website