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MA20225: Probability 2B

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Intermediate (FHEQ level 5)
Follow this link for further information on period slots Period: Semester 2
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: MA20225 Mandatory extra work (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites: Before taking this unit you must take MA20224
Follow this link for further information on unit content 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.
Follow this link for further information on programme availabilityProgramme availability:

MA20225 is Compulsory on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 2
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 2
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 2
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 2
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

MA20225 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 2
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 2
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 2
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 2
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 2
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.