M3S9
Department of Mathematics
Question
Q 1
Q 2
Stochastic Simulation
Examiner's Comments
The question contained material that most students were familiar with, thus showing good
performance. For parts (a), (b), (c) and (d)(i) variation in the marks was mainly due to deriving a
rigourous mathematical formulation and explaining the definitions carefully. Part (d)(ii) required
applying a theorem from the lecture notes to a novel problem and most of the students performed
very well in uncovering this link and providing a full proof as required.
This question turned out to be difficult and challenged the students. For part (a) (i) and (ii), most of
the students had problems in deriving the complete proofs as required. However, performance for
part (iii) was strong, showing that students were well familiar with the rejection sampling
algorithm. Altogether, lower performance for (i) and (ii) was surprising as the material was
classified as seen. Part (b) was well performed and required mainly familiarity with the lecture
notes. Part (c) contained unseen material and this was reflected in the performance accordingly.
Only few students performed well, applying the course content to a new problem, but most
students were unable to derive meaningful solutions or leaving blank answers altogether.
Similarly to question 2, this question challenged the students and resulted in a large variation in the
marks. Part (a) was overall well performed. Part (a) (iii) contained unseen material and it was good
to see that most of the students correctly applied the pre-testing principle for the algorithm. Part
(b) showed larger variation, especially for part (i). A large proportion of students were unable to
correctly formulate the complete density for the proposal distribution. Further, for (ii) and (iii)
variation in performance was mainly due to completeness and rigour.
Q 3
Printed: 27/07/2018 11:48:09
M4S9
Department of Mathematics
Question
Stochastic Simulation
Examiner's Comments
For this mastery question, part (a) challenged the students, whereas parts (b) and (c) showed
smaller variation in the marks. Part (c) shows that although students were well familiar with the
mastery material they faced more difficulties for parts (a) and (b) due to incomplete
mathematical rigour.
Q 4
Printed: 27/07/2018 11:48:09

欢迎咨询51作业君