Class 28: Revision exercises of chaps. 3-5

17 dezembro 2013, 08:00 • Manuel Cabral Morais

Exercises: GV-4Fev2010- (a)(b) [Chap. 3], GIV-19Jan2010-(a)(b) [Chap. 4], 4.120, GVIII-10Jan2011-Exercise 1 [Chap. 5], 5.145

Class 27: Chap. 5

16 dezembro 2013, 13:00 • Manuel Cabral Morais

Chap. 5 - Convergence concepts and classical limit theorems

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 revisited), 5.171 (Bernoulli; Exponential revisited and Mathematica), 5.185(a), 5.188, 5.199

Class 26: Chap. 5

10 dezembro 2013, 08:00 • Manuel Cabral Morais

Chap. 5 - Convergence concepts and classical limit theorems

5.8 Characteristic functions (-> Theorem 5.183)

Exercises: 5.160, 5.162(b)(d), 5.167(b), 5.171(b)

Class 25: Chap. 5

9 dezembro 2013, 13:00 • Manuel Cabral Morais

Chap. 5 - Convergence concepts and classical limit theorems

5.6 Weak law of large numbers (Exercise 5.131 -> end)

5.7 Strong law of large numbers

Exercises: 5.131, Proof Theorem 5.132, 5.134, 5.137, 5.146, 5.148, 5.156

Class 24: Chap. 5

3 dezembro 2013, 08:00 • Manuel Cabral Morais

Chap. 5 - Convergence concepts and classical limit theorems

5.4 Convergence of random vectors

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 (-> Exercise 5.130)

Exercises: GVIII-10Jan2011-Exercise2, 5.112, 5.114, Example/Exercise 5.125(c), 5.130