Portale di Ateneo - En.Unibs.it

Introduction to Statistics

Data collected and descriptive statistics: organization and description of data. Populations and samples. Normal samples.

Elements of probability

Combinatorial analysis. Introduction to the concept of probability. Sample space and events. Axioms and properties of probability. Conditional probability. Theorem of total probability and Bayes' formula. Independent events.

Models of random variables

Analysis of some one-dimensional random variables: Bernoulli random variables, binomial, hypergeometric, Poisson, geometric, rectangular, normal, exponential, gamma, chi-square, Student's t. Approximations.

Multivariate random variable

Joint distribution for discrete random variables. The multinomial distribution. Independent random variables. Conditional distributions. Joint distributions of functions of random variables. Covariance and correlation.

The distribution of sample statistics

Sampling and statistics. The sample mean. Limit theorems. The sample variance. The distributions of the statistics of normal populations.

Parameter estimation

Point estimates of parameters: research methods. Estimators and their properties. Interval estimation: confidence intervals (normal case).