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Mathematics and Statistics turn 2
Code: G271BB
Teacher:  Lucia Baldi
CFU subdivision: Lectures: 3
Practices in classroom: 1
Basic aims:  Knowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals).Knowledge of descriptive statistics. Knowledge of the position and variability indicators. Knowledge of methods of inferential statistics. Acquisition of the principles and techniques of regression and correlation between various parameters.
Acquired skills:  Possibility of exploiting the basic tools of Maths in any context. Describe the phenomena by the main statistical indicators; plan sample surveys; use the methodology of the analysis of variance at 1 and 2 factors; understand the results of statistical surveys.
Course contents:  CFU 1 - Definitions of statistical variables, graphical representations, mode, median, mean and variability; statistical variables in two dimensions. CFU 2 - Probability, random variables, sampling, estimators, binomial, Gaussian, Student t, Fisher F and Chi-square distribution, confidence intervals, testing hypotheses. CFU 3 - Analysis of Variance, CFU 4 - Regression, correlation.
Program:  1- The language of statistics.
2- Organization of data end graphical representation.
3- Position and variability indices (mean, mode, median),
4- Bivariate analysis for qualitative or quantitive data.
5- Probability, probability rules. Independents events. Total
probability theorem. Bayes theorem.
6- Random variables, distributions. Distributions: binomial,
geometrical, Poisson, Gaussian.
7- Random samples. Confidence intervals. Estimation. Sample
mean. Central Limit Theorem. Confidence interval for the mean.
8- Hypothesis tests: fundamentals, phases, simple test.
9- Hypothesis test on a single population proportion.
10- Test and confidence interval for the difference of two means
using independent sample.
11- Correlation analysis. Univariate linear regression. Inference.
12- Analysis of variance.
Prerequisites:  The student should be familiar with mathematics
Preparatory instructions:  Mathematics
Learning materials:  Introduzione alla Statistica, di M. K. Pelosi e T. M. Sandifer, ed.
McGraw-Hill, 2009
Other info:  The exam is based on 75' written test. An oral exam is required if
the result of the written one is 16 or 17 /30. The oral exam is not
cumpulsory if the result of the written test is 18/30 or more.
Program of Mathematics and Statistics turn 2 (pdf version)
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