29596 - Probability And Statistics

Learning outcomes

The aim of the course is to refresh the pre-requisite knowledge for the STATISTICS course, usually acquired by the student in his/her first cycle degree. At the end of the course the student has a working knowledge of: -probability, conditional probability, probability distributions, sampling distributions, estimation methods (moments, likelihood) and large sample theory.

Course contents

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.

Readings/Bibliography

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.

Teaching methods

Classroom lessons

Assessment methods

Written multiple-choice self-assessment test.

Teaching tools

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

Office hours

See the website of Pier Giovanni Bissiri