30456 - STATISTICS - MODULE 1 (THEORY AND METHODS)
Course taught in English
Go to class group/s: 13
- Basic exploratory data analysis: frequency distributions, graphical representations, summary statistics of central tendency and variability.
- Probability: elementary set theory, events, algebras, axiomatic definition, conditional probability and elementary rules of calculus.
- Random variables: discrete and continuous distribution, expectation and moments, common families of distributions (Bernoulli, binomial, Poisson, normal, negative exponential, gamma).
- Random vectors: joint, marginal and conditional distributions, covariance and correlation coefficient, stochastic independence.
- Functions of random variables.
- Sampling: population and sample, inferential process, sample variability and sampling error, statistics.
- Sample mean: expected value and variance, distribution for normal and Bernoulli population, central limit theorem and convergence in distribution.
- Sampling from the normal distribution: sample variance and the Chi-square distribution, t-distribution.
- Point estimation: method of moments, maximum likelihood. Properties of estimators: unbiasedness, consistency and mean squared error.
- Two partial written exams (one in the middle and one at the end of the course), with exercises and questions about theory;
- A written general exam with exercises and questions about theory.
- M. W. TROSSET, An Introduction to Statistical Inference and Its Applications with R, Chapman and Hall/CRC, 2009.
- Additional material is provided online.