Elements of Probability and Statistics

Description

Subject objectives: Introduce students to the tools of exploratory data analysis and probability theory. Provide an introduction to the open-source software R for performing descriptive analyses and generating probabilistic models. Contents: Descriptive statistics for one variable (5 lecture hours). Introduction to descriptive statistics. Types of data and variables. Frequencies. Measures of location, dispersion and shape. Graphic tools of descriptive analysis of one variable. Two-dimensional descriptive statistics (4 lecture hours). Joint distribution of frequencies. Tables. Marginal and conditional frequencies. Graphic tools for two variables. Linear dependence. Regression lines. Covariance and correlation. Probability Calculus (7 lecture hours). Probability space. Events. Probability. Properties. Conditional probability. Independence. Law of total probability. Bayes' theorem. Combinatorics One-dimensional random variables (5 lecture hours). Random variable. Distribution function. Types of random variables: Discrete and continuous. Mass probability function and density function. Characteristics of a random variable. Transformation of random variables. Main models of probability (7 lecture hours). Discrete: Uniform, Bernoulli, Binomial, Poisson, Hypergeometric, Geometric, Negative Binomial. Continuous: Uniform, Normal, Exponential, Gamma, Beta. Relations of interest between the distributions. Contents of the laboratory classes (14 laboratory hours). The statistical package R. Exploratory data analysis. Generation of probability models with R.