30456 - STATISTICS - MODULE 1 (THEORY AND METHODS)
BESS-CLES
Department of Decision Sciences
Course taught in English
Go to class group/s: 13
Course Director:
CHIARA GIGLIARANO
CHIARA GIGLIARANO
Course Objectives
The course covers the main concepts of statistical thinking, both descriptive and inferential. The most relevant techniques for collecting and analyzing data are first explored. The course then introduces the fundamental principles of probability theory and random variables, as a basis for better understanding the point estimation theory. The focus is on analyzing real data, illustrating some of the methods and concepts with the help of the statistical software R.
Intended Learning Outcomes
Course Content Summary
The course focuses on the following main points
- Basic exploratory data analysis: frequency distributions, graphical representations, summary statistics of central tendency and variability.
- Probability: elementary set theory, events, algebras, axiomatic definition, conditional probability and elementary rules of calculus.
- Random variables: discrete and continuous distribution, expectation and moments, common families of distributions (Bernoulli, binomial, Poisson, normal, negative exponential, gamma).
- Random vectors: joint, marginal and conditional distributions, covariance and correlation coefficient, stochastic independence.
- Functions of random variables.
- Sampling: population and sample, inferential process, sample variability and sampling error, statistics.
- Sample mean: expected value and variance, distribution for normal and Bernoulli population, central limit theorem and convergence in distribution.
- Sampling from the normal distribution: sample variance and the Chi-square distribution, t-distribution.
- Point estimation: method of moments, maximum likelihood. Properties of estimators: unbiasedness, consistency and mean squared error.
Teaching methods
Assessment methods
Detailed Description of Assessment Methods
The exam can be taken in two alternative ways.
- Two partial written exams (one in the middle and one at the end of the course), with exercises and questions about theory;
- A written general exam with exercises and questions about theory.
Textbooks
- M. W. TROSSET, An Introduction to Statistical Inference and Its Applications with R, Chapman and Hall/CRC, 2009.
- Additional material is provided online.
Prerequisites
Knowledge of methods and concepts introduced in the course Mathematics - Module 1 (Theory and Methods).
Last change 14/06/2017 15:52