The course introduces students to statistical data analysis. It is intended to provide basic knowledge of descriptive and inferential statistics. Part of the course will be devoted to the study of the basic tools and the probabilistic mathematical language.
At the end of the course the student will be able to understand and interpret basic statistical analyses and should also be aware of the limits of the information obtained from the data.
Course Prerequisites
The contents of the course Analisi Matematica I
Teaching Methods
Lectures and sessions of practical exercises aimed at applying in concrete examples the theoretical concepts presented during the lectures.
Assessment Methods
There will be a written examination, where the student will be asked to solve some problems on the specific topics treated during the course. If the student is positively evaluated in the written examination, the commission or the student can ask for an additional oral colloquium.
Note that the final grade of "Complementi di Analisi Matematica e Statistica" will be the mean of the grades of the two parts of the course, "Complementi di Analisi Matematica" and "Statistica''.
Texts
M. Bramanti. Calcolo delle Probabilità e Statistica. Teoria ed Esercizi. Esculapio.
Contents
Part I: descriptive statistics. Data, populations and samples. Frequencies, percentages, histograms. Empirical mean, median, mode, quantiles, variance, standard deviation. Correlation coefficient (Pearson), scatter plots.
Part II: probability. Definition of probability, elements of combinatorics, conditional probability, independence, Bayes's formula. Applications to clinical tests and genetics. Discrete random variable: density and distribution function. Mean and variance. Binomial and Poisson distributions. Random discrete vectors: joint density and independence. Continuous random variables. Uniform, exponential and Gaussian (or normal) distributions. Density function, mean and variance. Independence. Properties of Gaussian random variables. Chebychev's inequality and law of large numbers. Central limit theorem and some applications. Part III: statistical inference. Random variables associated to a population. Point estimation and confidence interval. Sample mean random variable and sample standard deviation random variable. Confidence interval for the mean. Use of Student's t random variable. Confidence interval for a proportion. Hypothesis test for the mean. Null hypothesis. z-test and t-test. p-value. Hypothesis test comparing means of different populations. Chi-square test goodness of a fit. Chi-square test of independence. p-value. Linear regression.
Course Language
Italian
More information
This course is a part of "Complementi di Analisi Matematica e Statistica''
