Statistics II

Recommended Prerequisites

n.a.

Teaching Methods

Theoretical lectures: These lectures consist mainly on the oral presentation of subjects, frequently motivated by introductory questions and examples. The oral presentation is accompanied by data show projection of schematic texts.

Applied lectures: problem solving. Each exercise starts with its solving by students; then, its solution is projected using data show. Occasionally, the resolution is preceded by a brief presentation of the theoretical framework.

Learning Outcomes

Overall objectives and Generic competencies:

Understanding of the notion of probabilistic model. Understanding of basic notions of statistical inference.

Application of these concepts in simple situations in the area of Economics and business administration.

Specific objectives and Specific competencies:

Knowledge of probability theory at an undergraduate level and understanding of the notion of probabilistic model. Common discrete and continuous probabilistic models. Point estimation (methods of moments and of maximum likelihood). Understanding of the notion of confidence intervals and hypotheses tests, namely under Gaussian models. Understanding of the main asymptotic results (law of large numbers and central limit theorem) and its application to statistical inference. Application of these concepts to simple economic and business problems.

Work Placement(s)

No

Syllabus

1 Random variable (rv). Distribution function. Classification of rv’s. Functions of a rv. 1.5 Bivariate rv’s. 2 Discrete distributions. Moments. Moment generating function (mgf). Distributions: uniform, Bernoulli, binomial, geometric, negative binomial and Poisson. 3 Continuous distributions. Moments. Order statistics. Mgf. Distributions: uniform, normal, exponential and chi-squared. Central limit Theorem. 4 Sampling. Sampling distributions. Probability and statistical inference. Random sampling. Statistics. Sampling distributions. Sample average and variance. Asymptotic sampling distributions. Normal population: distribution of the sample average. Normal population: distribution of the sample variance. Student-t ratio. 5 Estimation. Methods of point estimation. Properties of estimators. Interval estimation. 6 Hypotheses tests. Most powerful test. Neyman-Pearson Lemma. Simple versus joint hypotheses. P-value. Normal population: tests of the mean and variance. Large sample tests.

Head Lecturer(s)

José Maria Ruas Murteira

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

Murteira, B., C. Silva Ribeiro, J. Andrade e Silva, C. Pimenta (2010), Introdução à Estatística, Escolar Editora.