Each question counts 10 points, making a total of 110 points. The exam will be graded on the scale of the Norwegian Mathematics Council, converted to 110 points:
A: 110-101
B: 100-84
C: 83-64
D: 63-50
E: 49-44
F: 43-0
The points will be supplemented by an overall assessment before the grade is set.
Comments on (some) individual problems:
1a) 4 points for setting up the problem correctly, 6 points for doing the calculations.
1b) No deduction for not checking that Y is integrable. Other methods (e.g. calculating the Moment Generating Function) are accepted.
1e) It is not necessary to check the continuity of the limit function - the continuity follows from the fact that it is the characteristic function of Y.
2a) The main point is to find the values for p, but we will deduct a few points if there is no mention of the other characteristics of a martingale (adaptedness and integrability).
2b) As there was a mistake in the (original) version of the problem, we will be lenient here and concentrate on the main ideas. 2 points will be deducted for not getting sharp inequalities.
3b) 4 points for the inequality and 6 six points for the calculations.
3d) 5 points for a clear description of how the Borel-Cantelli lemma can be applied to this problem. For full score it is not sufficient to say that the series converges according to the hint, one also has to show how the hint can be used.