Programa

Probability and Statistics

Licenciatura Bolonha em Gestão

Licenciatura Bolonha em Economia

Programa

1. Probability: Kolmogorov axioms, conditional probability, independent events. 2. Random variables: cumulative distribution function, discrete and continuous random variables. 3. Expected values and parameters: mean value, variance, quantiles, median. 4. Bivariate random variables: joint distribution and marginal distributions. Independence. Covariance. 5. Important distributions: binomial distribution and Poisson distribution. Continuous uniform distribution. Exponential distribution. Gaussian distribution. 6. Probability versus statistics. The concept of random sample and the concept of statistic. Properties of the sample mean and of the sample variance. 7. Sampling distribution of the sample mean and of the sample variance in the context of a Gaussian population. Chi-square and Student-t distributions. Large samples: central limit theorem. 8. Point estimation. Properties of estimators. The maximum likelihood method and the method of moments. 9. Interval estimation: basic ideas. Pivotal quantity. The construction of confidence intervals in the context of a Gaussian distribution. The case of large sample sizes. 10. Hypotheses testing: basic ideas. Type I and type II errors in the context of simple hypotheses. Tests for composite hypotheses. P-value. Hypotheses testing in the context of a Gaussian population. Large sample sizes.