Università Roma Tre

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Entropy. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Benjamin-Cebicev inequality. Variance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.
Least-squares and regression. Goodness of fit of a regression line.

Axioms of elementary probability. Elementary theorems of probability. Mutually exclusive events. Conditional probability. Independence. Bayes theorem. Discrete random variables. Expectation. Bernoulli distribution. Binomial distribution and random walk. Hypergeometric distribution. Poisson distribution.
Continuous random variables. Probability density. Normal distribution. Normal tables. Normal approximation to the binomial distribution. Student's t.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean, the variance and the proportion. Confidence intervals. Confidence intervals of a single mean and of the difference between two means. Confidence interval of a proportion and of the difference between two proportions. Optimal sample size.

Alan Agresti, Christine A. Franklin and Bernhard Klingenberg (2017) Statistics: The Art and Science of Learning from Data (4th Edition) ISBN 978-0321997838