31 lezioni di probabilità e statistica
About the CourseCombinations and dispositions, probability space, conditional probability, independent events, total probability formula, Bayes formula. Notions of random variables (discrete and absolutely continuous), of mean and variance, standardization. Covariance and linear correlation of two variables, independent variables. The binomial, Poisson and normal distributions and the t, chi square and F distributions. Population, samples, data functions and relative degrees of freedom. Confidence intervals by average and by proportion. First and second species errors, tests on a proportion, on an average, on the difference of two averages, on several proportions, on the ratio of variances; furthermore, the calculation of the value "p" by means of R. Square line, linear correlation coefficient, linear determination coefficient. Linear dependence test in terms of F ratio and in terms of Student's t (Pearson test). Using R implementation of the Kolmogorov-Smirnov test on residual normality, as well as confidence intervals of the angular coefficient and correlation.
- Know the basics of probability, the binomial and Poisson distributions, the normal, t, chi squared and F distributions.
- Trace from one or two samples to the population parameters by means of confidence intervals and parametric tests, under a given significance level. In particular, test a proportion, an average, a difference in averages, several proportions, a ratio of variances.
- To be able to treat simple linear regression in the aspects of linear dependence tests, confidence intervals, normality test for the residues, linear correlation.
Background and RequirementsThe prerequisites: knowledge of analytical geometry and graphs of elementary functions such as powers, roots, exponentials and logarithms; knowledge of the derivatives and primitives of elementary functions, with the calculation of their definite integrals.
Sheldon Ross, Probabilità e statistica per l’Ingegneria e le Scienze, Milano 2008.