# Course detail

### LCE5806 - Mathematical Statistics I

__Credit hours__

In-class work per week |
Practice per week |
Credits |
Duration |
Total |

3 |
1 |
8 |
15 weeks |
120 hours |

__Instructor__

Edwin Moises Marcos Ortega

Idemauro Antonio Rodrigues de Lara

Renata Alcarde Sermarini

__Objective__

To enable the students in topics of Probability Theory and Statistical Inference.

__Content__

1. Algebra and sigma-algebra of random events. 2. Basic principles of probability theory: axioms and theorems. 3. Random variable, distribution function, distribution function and probability density function. 4. Probability models families. 5. Random Vectors, joint cumulative function, marginal and conditional functions, independence of random variables. 6. Expectation mathematic, variance and covariance, conditional expectation, expectation of random vector, moment generating function. 7. Transformations of random variables: cumulative function, Jacobian and moment gernerating functions techniques. 8. Basic concepts of inference, random sample and properties, order statistics, and sample distributions. 9. Principles of data reduction, sufficient and complete statistics, k-parametric exponential family. 10. Point estimation methods: least squares, moments and maximum likelihood. 11. Properties and comparison of estimators, uniformly minimum-l variance umbiased estimator, mean- squared-error, Rao-Blackwell and Lehmann Scheffé theorems. 12. Interval estimation: random intervals for parameters associated with normal random variables, pivotal quantity method. 13. Introduction to hypothesis tests: basic concepts, error- types and power function, Neyman-Pearson lemma, uniformly more powerful tests, likelihood ratio test.

__Bibliography__

1. Casella G.; Berger L.R. Statistical Inference. 2nd. Edition, Duxbury Press, 2002.

2. Degroot, M.H. Probability and Statistics. 4th. Edtion, Addison-Wesley, 2011.

3. James, B.R. Probabilidade: um curso em nível Intermediário. Projeto Euclides, RJ, 2008.

4. Magalhães, M.N. Probabilidade e Variáveis Aleatórias. 3ª Edição São Paulo, IME/USP, 2015.

5. Murteira, B.J.F. Probabilidade e Estatística. vol I, II. 2ª Edição, McGraw-Hill, Portugal, 1990.

6. Mood, A.M.; Graybill, F.A. and Boes, D. Introduction to the Theory of Statistics. 3rd. Edition, McGraw-Hill, 1974.

7. Roussas, G.G. A Course in Mathematical Statistics. 2nd. Edition: Academic Press, 1997.

8. Sheldon, R. Introduction to Probability Models. Academic Press, 2014.

9. Zwanzig, S. Introduction to the Theory of Statistical Inference. Taylor & Francis, 2011.