29596 - PROBABILITY AND STATISTICS

Contenuti

Probability concepts:

Review of the axiomatic approach to probability Total Probability Law and Bayes Theorem

Discrete and continuous random variables and properties of some common families of probability distributions

Joint and marginal distributions, conditional distributions and independence, expected values, covariance and correlation

Statistical inference

Random sampling and sampling distributions. The likelihood function.

Estimation theory. Point estimation: finite estimator properties. Interval estimation. Moments and maximum likelihood estimation method. Asymptotic properties of the maximum likelihood estimators.

Module 2:

Hypothesis tests: Statistical tests about the mean, a proportion, the variance of a population. Approximate test on a probability. Test on the difference between two means. Test on the difference between two proportions. Test on the difference between two variances. The concept of p-value. Chi square test.

Testi/Bibliografia

Larsen R.J. and Marx M.L. (2012) "An introduction to mathematical statistics and its applications", Prentice Hall.

Casella, G. and Berger, R.L. (2002). Statistical Inference, Wadsworth.

Teacher's notes.

Metodi didattici

Classroom lessons

Modalità di verifica e valutazione dell'apprendimento

Written multiple-choice self-assessment test.

Strumenti a supporto della didattica

Teacher's notes available at the web-site https://virtuale.unibo.it/

Orario di ricevimento

Consulta il sito web di Pier Giovanni Bissiri