Instructions:


Your regular assessment will be on the 16th of December at 9:00 (please confirm on Fenix).

The duration of the exam is 2h30m. The exam has two parts.

Part I:
you should complete direct sentences in order to obtain true propositions. You should answer on the exam paper.
 
The items are independent from each other. There is no need to justify your answers unless the questions ask to do so. For each item you should spend no more than 2-3 minutes.

Part II 
 You should show all computations and give short justifications.

Question 1: Sets and measure.
Proof of a short item discussed in the Lectures.

Question 2:
Use Convergence Theorems
 (Fatou Lemma, Monotone Convergence or Dominated Convergence).

Question 3:
Distributions and Distribution Functions.

Question 4:
Conditional Expectation.

Question 5:
Limit Theorems, Independence and Distributions.
Use the Law of Large Numbers.

You should bring official sheets of exams (from ISEG) for the Part II.
Calculators are not allowed. Mobile phones and digital clocks should be kept out of students' reach.