Department of Mathematical Sciences, Unit Catalogue 2010/11 |
MA20225: Probability 2B |
 Credits:
| 6 |
| Level:
| Intermediate |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX100 |
| Supplementary Assessment: | Supplementary assessment information not currently available (this will be added shortly) |
| Requisites:
| Before taking this unit you must take MA20224 or equivalent units from MA10001 - MA10006. You may not take this unit if you have already taken MA20036. |
| Description:
| Aims: To present a formal description of Markov chains and Markov processes, their qualitative properties and ergodic theory. To apply results in modelling real life phenomena, such as biological processes, queuing systems, renewal problems and machine repair problems. Learning Outcomes: After taking this unit, students should be able to: * Classify the states of a Markov chain; * Find hitting probabilities, expected hitting times and invariant distributions; * Calculate waiting time distributions, transition probabilities and limiting behaviour of various Markov processes. Skills: Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F (in tutorials). Content: Markov chains with discrete states in discrete time: Examples, including random walks. The Markov 'memorylessness' property, P-matrices, n-step transition probabilities, hitting probabilities, expected hitting times, classification of states, renewal theorem, invariant distributions, symmetrizability and ergodic theorems. Markov processes with discrete states in continuous time: Examples, including Poisson processes, birth & death processes and various types of Markovian queues. Q-matrices, waiting time distributions, equilibrium distributions and ergodicity. |