In week #1 we reviewed some material from Probability Models and introduced renewal processes.

In week #2 we continued with renewal processes.

In week #3 we introduced Poisson processes.

In week #4 we discussed the Renewal Rewards Theorem and its implications.

In week #5 we discussed semi-Markov processes.

In week #6 we proved a result about conditioning a Poisson process on the value of N(t) and introduced continuous time Markov chains.

Week #7 is Reading Week and there are no lectures or exercise classes.
You should take this time to review your notes and the problem sheets.
The problems on side 2 of Problem Sheet #5 will be covered in Week #8.

In week #8 we characterized continuous time Markov chains and defined the generator.

In week #9 we investigated the limiting distributions of continuous time Markov chains.

In week #10 we introduced Brownian Motion.

In week #11 we discussed the invariance and reflection principles.

In week #12 I made some remarks about the final exam. It will consist of five questions, each worth 20 marks, all of which you should do. Each question will be on one topic. You can expect a question on semi-Markov processes or conditioning the value of a Poisson process on N(t). There won't be a question on discrete time renewal theory, as we did not cover that in detail.

The exams from these years covered material similar to what we covered, except in these exams there is a question on discrete renewal theory. Our exam will be in the same format as these exams: five questions with one topic per question.