Introduction to biomedical statistics

Introduction to biomedical statistics

Facoltà di Scienze Matematiche Fisiche e Naturali

Facoltà di Ingegneria dell'Informazione, Informatica e Statistica

Facoltà di Medicina

Topic: Probability and Statistical Inference.

Reception: Via Regina Elena 295, building G, first floor.To make an appointment, please mail me at costantino.ricciuti@uniroma1.it

Book: Sheldon Ross: "Introduction to probability and statistics for engineers and scientists".

Exam: The exam consists in a written test, including exercises and some theoretical questions. Moreover, if I deem it appropriate, a brief oral interview may also take place.

Dates of written exams:

Pre-exam: May 24, 2019 (10.00 a.m.)

First Exam: June 10, 2019 (10.00 a.m.)

Second Exam: July 10, 2019 (10.00 a.m.)

Third Exam: September 24, 2019 (02.00 p.m.)

Fourth Exam: February 25, 2020 (10.00 a.m.)

Programme of the lessons:

05/03/2019: Presentation and description of the course. Experiments with non deterministic outcome: sample space and events, union and intersection of events.

08/03/2019: Axioms of probability and their consequences. Basic principle of counting, elements of combinatorics.

12/03/2019: Sample spaces with equally likely outcomes. Conditional probability.

15/03/2019: Independent events. Law of total probability. Bayes theorem.

22/03/2019: Exercises.

27/03/2019: Random variables. Discrete distributions. Probability mass function. Expected value. Discrete density and mean value of functions of discrete random variables.

29/03/2019: Variance of a random variable. Expected value and variance of Y=aX+b. Bernoulli trials, Binomial distribution.

03/04/2019: Continuous distributions. Density function. Expected value and variance. Exponential and uniform distributions.

05/04/2019: Normal distribution. Discrete joint distributions.

10/04/2019: Exercises.

12/04/2019: Basic notions on random vectors. The central limit theorem.

16/04/2019: Basic notions of descriptive statistics: data samples, histograms, sample mean and sample variance. The problem of statistical inference. Population, random samples, distributional properties of the sample mean and the sample variance.

17/04/2019: Parametric and non-parametric inference. Basic notions on point estimators.

26/04/2019: Exercises.

29/04/2019: Interval estimation for the mean of a normal population with known variance.

03/05/2019: The t-Student distribution. Interval estimation for the mean of a normal population with unknown variance. Interval estimation for an unknown proportion.

08/05/2019: General notions on hypotesis testing. The z-test.

10/05/2019: Exercises.

15/05/2019: The t-test. Remarks and examples on hypotesis testing.

16/05/2019: Exercises.