Learning outcomes of the course unit
Understanding and capability to communicate the foundation of probability theory, and of descriptive and inferential statistics. Knowledge and application of technical tools regarding regression models and statistical testing.
Course contents summary
Descriptive statistics. Inferential statistics. Elements of probability theory. Discrete and continuous random variables. Central limit theorem. Parameter estimation. Confidence levels. Statistical hypothesis testing. Regression.
Data organization e description, mean, median, mode, histograms, variance and standard deviation.
Normal model and correlation.
Sample space and events, probability axioms, binomial coefficient, conditional probability, Bayes' formula, independent events.
(approx. 6 hours)
Continuous and discrete random variables, joint and conditional distributions, expected value, covariance, moment generating function.
Random variable models: Bernoulli, Poisson, hypergeometric, binomial, uniform, normal, exponential, gamma, chi-square, t, F.
(approx. 22 hours)
Sample meand, central limit theorem, sample variance.
Maximum likelihood estimators, confidence intervals, bayesian estimators.
Significance levels, mean and variance testing, t-test, hypothesis tests in Bernoulli populations and on the mean of Poisson distributions.
(approx. 28 hours)
Regression parameters estimation, inferential statistics, estimators distributions, transforming to linearity, weighted least squares.
(approx. 16 hours)
Sheldon M. Ross
Introduction to probability and statistics for engineers and scientists
Elsevier, fifth edition, 2014
Classroom lectures and exercises.
Homework exercises and (possible) projects.
Software use (Matlab) for problem resolution.
Assessment methods and criteria
Written exam with possible supplementary oral.