Class 41: Chap. 5

17 dezembro 2010, 08:00 • Manuel Cabral Morais

Chap. 5 - Convergence of sequences of random variables

5.1 Modes of convergence

5.1.1 Convergence of r.v. as functions on Omega (Exercise 5.4 -> end)

5.1.2 Convergence in distribution (->Example 5.28)

To read at home:

5.1 Modes of convergence

5.1.2 Convergence in distribution (Exercise 5.29 -> end)

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]

Exercises: 5.4 hint, 5.11, 5.16, 5.18 hint, 5.21.

Class 40: Chaps. 4 and 5

16 dezembro 2010, 08:00 • Manuel Cabral Morais

Chap. 4 - Expectation

4.6 Moments

4.6.7 Multivariate normal distributions (Exercise 4.204(c) - correction)

4.6.8 Multinomial distributions

Exercises: 4.204(c) - correction, 4.212.

Chap. 5 - Convergence of sequences of random variables

5.1 Modes of convergence

5.1.1 Convergence of r.v. as functions on Omega (-> Remark 5.3)

Class 39: Chap. 4

14 dezembro 2010, 08:00 • Manuel Cabral Morais

Chap. 4 - Expectation

4.6 Moments

4.6.7 Multivariate normal distributions (Corollary 4.191 -> Exercise 4.204(c))

Exercises: 4.170, 4.199(a), 4.204(c).

Class 38: Chap. 4

10 dezembro 2010, 08:00 • Manuel Cabral Morais

Chap. 4 - Expectation

4.6 Moments

4.6.5 Correlation (Prop. 4.169 -> end)

4.6.6 Moments of random vectors

4.6.7 Multivariate normal distributions (-> Corollary 4.191)

Exercises: 4.171, 4.178, 4.185 hint.

Class 37: Chap. 4

9 dezembro 2010, 08:00 • Manuel Cabral Morais

Chap. 4 - Expectation

4.6 Moments

4.6.2 Variance and standard deviation

4.6.3 Skewness and kurtosis

4.6.4 Covariance

4.6.5 Correlation (-> Exercise 4.168)

Exercises: 4.143 hint, 4.144 hint, 4.155(a), 4.166 hint, 4.167, 4.168.