MI-669  Probabilidade avançada
Programa:



Bibliografia:
  1. A.N. Shiryaev "Probability"
  2. R. Durrett "Probability: theory and examples"
  3. S. Resnick "A probability path"
 



Sugestão de exercícios:

Resnick, cap. 1:  1 - 6, 8, 9, 11, 12, 14 - 24, 26, 27, 30, 31, 32 (difícil), 34, 36, 37, 41, 42.
Resnick, cap. 2:  1, 5, 8, 13, 16, 18, 19, 21, 22.
Resnick, cap. 3:  1 - 9, 11, 12, 14, 15, 18, 25 (falta \ge k entre [] no item (a))
Resnick, cap. 4:  1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 24.

Resnick, cap. 5:  1, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 15, 19, 22, 24, 30, 35, 38.
Resnick, cap. 10: 1, 2, 3, 4, 6, 7.
Resnick, cap. 6: 1(a), 5, 6, 8, 10, 11 (a), 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
Resnick, cap. 7: 1, 2, 5, 6, 8, 9, 11, 12, 13, 14, 15, 17, 18, 20, 28, 33, 36, 37, 38, 39, 40, 41, 42.

Resnick, cap. 8: 3, 4, 10, 12, 13, 17, 18, 31, 32.

Resnick, cap. 9: 2, 34, 5, 6, 7 (erro na dica: Y_n=X_n \1_{|X_n|\le \sqrt{n}\ln n}), 10, 12, 16, 17, 33, 34, 35, 46.


Shiryaev ((c)-tais que limite de x_n existe e é finito; (f) - para pelo menos um n).