31 lezioni di probabilità e statistica
About the Course
Combinations 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.Computer and Data Sciences
Training hours20
LevelBeginner
Tutored
Italiano
Duration8 weeks
TypeOnline
Self Pacement
Course Agenda
Course Opens
Course Closes
Learning outcomes
- 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 Requirements
The 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.Textbooks
Sheldon Ross, Probabilità e statistica per l’Ingegneria e le Scienze, Milano 2008.
Course Format
The course is structured in 31 video lessons, also available in pdf format that the student is invited to study in full. In each lesson we require a certain mathematical attention, in the sense of clearly distinguishing between definitions, propositions or theorems, possible proofs, always with at least one example or application carried out in full. After the text of each lesson, the text of some exercises is proposed in pdf only, which the student is invited to perform before moving on to the next lesson. Preference is given to the use of numerical tables for statistical distributions, which are also attached in pdf. The use of the R software is reduced to the essential.Certificates and Exam rules
Attendance Certificate
In order to obtain the attendance certificate and the open badge, the student will have to pass the two questionnaires in the course.
