Class 27: Chap. 5 Modes of convergence

16 dezembro 2014, 08:00 • Manuel Cabral Morais

5.7 Strong law of large numbers (Theorem 5.155 -> end)

5.8 Characteristic functions

5.9 The Central Limit Theorem

5.10 The law of the iterated logarithm 5.11 Applications of the limit theorems Exercises: 5.160 (Exponential), 5.167(b), 5.185(a); 5.188 (coincides with GIII-10Jan2014-Exercise 3(a)); 5.199

Class 26: Chap. 5 Modes of convergence

15 dezembro 2014, 13:00 • Manuel Cabral Morais

5.4 Convergence of random vectors (GVIII-10Jan2011-Exercise2)

5.5 Limit theorems for Bernoulli summands

5.5.1 Laws of large numbers for Bernoulli summands

5.5.2 Central limit theorems for Bernoulli summands

5.5.3 The Poisson limit theorem

5.6 Weak law of large numbers

5.7 Strong law of large numbers (-> Theorem 5.153)

Exercises: GVIII-10Jan2011-Exercise2; 5.112, Example/Exercise 5.125(c); 5.134, GIII-Test2-10Jan2014-Exercise 2 (after Theorem 5.143), 5.146; 5.148

Class 25: -

9 dezembro 2014, 08:00 • Manuel Cabral Morais

Docente em deslocação ao estrangeiro (Missão: IST/2014/M2322) para apresentar trabalho na "7th International Conference of the ERCIM Working Group on Computational and Methodological Statistics - ERCIM/2014” na Universidade de Pisa, Itália

Class 24: Chap. 5 Modes of convergence

2 dezembro 2014, 08:00 • Manuel Cabral Morais

5.1 Modes of convergence

5.1.3 Alternative criteria

5.2 Relationships among the modes of convergence

5.2.1 Implications always valid

5.2.2 Counterexamples

5.2.3 Implications of restricted validity

5.3 Convergence under transformations

5.3.1 Continuous mappings

5.3.2 Algebraic operations

5.4 Convergence of random vectors

Exercises: 5.64 (GVIII-4Fev2010), 5.68 (GVIII-19Jan2010), 5.73, 5.82 (a.s.), 5.85 (q.m.), 5.99

Class 23: Chap. 5 Modes of convergence

1 dezembro 2014, 13:00 • Manuel Cabral Morais

5.1 Modes of convergence

5.1.1 Convergence of r.v. as functions on Omega

5.1.2 Convergence in distribution

Exercises: 5.4, 5.12, 5.16, 5.21, 5.30, GIII-Test2-10Jan2014-Exercise 1(b)