The course is designed to equip students in Economic and Business Sciences with an introduction to probability and to descriptive and inferential statistics.
Prerequisite to this module is the mastering of a few basic mathematical concepts such as limit, derivative and integration at the level of an undergraduate first year introductory course in calculus.
Descriptive Statistics: data collection and classification; data types; frequency distributions; histograms and charts; measures of central tendency; arithmetic mean, geometric mean and harmonic mean; median; quartiles and percentiles; fixed and varying base indices; Laspayres and Paasche indices; variability and measures of dispersion; variance and standard deviation; coefficient of variation; moments; indices of skewness and kurtosis; multivariate distributions; scatterplots; covariance; variance of the sum of more variables; method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficiente; deviance residual and deviance explained; multivariate frequency distributions; conditional distributions; chi-squared index of dependence; index of association C; Simpson’s paradox.
Probability: events, probability spaces and event trees; combinatorics; conditional probability; independence; Bayes theorem; discrete and continuous random variables; distribution function; expectation and variance; Markov and Tchebycheff inequalities; discrete uniform distribution; Bernoulli distribution; binomial distribution; Poisson distribution; geometric distribution; continuous uniform distribution; normal distribution; exponential distribution; multivariate discrete random variables; joint probability distribution; marginal and conditional probability distributions; independence; covariance; correlation coefficient; linear combinations of random variables; average of random variables; weak law of large numbers; Bernoulli’s law of large numbers for relative frequencies; central limit theorem.
Inferential Statistics: sample statistics and sampling distributions; chi-square distribution; Student-t distribution; Snedecors-F distribution; point estimates and estimators; unbiasedness; efficiency; consistency; estimate of the mean, of a proportion and of a variance; confidence intervals for a mean, for a proportion (large samples) and for a variance; hypothesis testing; one and two tails tests for a mean, for a proportion (large samples) and for a variance; hypothesis testing for differences in two means, two proportions (large samples) and two variances.
The course consists of a series of lectures (56 hours) and of twelve exercise classes (24 hours).
All classes are essential to a proper understanding of the topics of the course.
The working language is Italian.
|G. Cicchitelli, P. D'Urso, M. Minozzo||Statistica: principi e metodi (Edizione 3)||Pearson Italia, Milano||2018||9788891902788|
The final exam consists of a two-hours written exam paper containing both practical exercises and theoretical definitions and derivations. The oral part is voluntary and open to students who receive at least a mark of 15/30 in the written exam. Students can expect to gain/loose up to three marks with the oral examination.
An intermediate examination paper on the first part of the program is planned. Students who successfully pass the intermediate examination have the option of taking a similar paper on the second part of the module during the exam session immediately after the end of the course, rather than sitting the full final exam paper.