Unit_outline

Unit coordinator/lecturer: Dr Małgorzata O’Reilly

Prerequisites: KMA152 or KMA182 or equivalent with approval from HoS.

Unit description: This unit provides grounding in probability models, and develops skills in modelling of real-life systems with element of uncertainty, particularly useful for careers in the Physical and Biological Sciences, Engineering, Computer Science, Finance and Economics.

Topics include probability theory and stochastic processes, with the focus on developing in-depth knowledge both from a theoretical and a modelling point of view.

Probability theory

Sample space, event, probabilities on events, independent events, Bayes' formula
Random variable, probability distribution, expectation, conditional probability and conditional expectation
Distribution functions: discrete, continuous; joint distribution
Probability generating function; Laplace transform

Stochastic Processes

Bernoulii process
Poisson Process
Discrete-time Markov chains: Chapman-Kolmogorov equations, classification of states, recurrence, limiting probabilities
Continuous-time Markov chains: Kolmogorov differential equations, Embedded Chains, equilibrium distributions, Birth and Death Processes

Assessment: 3 hour exam (80%), assignments (20%)

References:

S. M. Ross, Introduction to Probability Models
G. Grimmett and D. Stirzaker, Probability and Random Processes
S. K. Karlin, A First Course in Stochastic Processes
W. Feller, An Introduction to Probability Theory and Its Applications, volume I

Flexible learning: All files can be accessed though MyLo. The files include lecture notes and audio files, amongst other material related to the unit.

School of Mathematics and Physics