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Module ST2351: Probability and Theoretical Statistics I
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Michaelmas term 2012-13
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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Prof. Simon Wilson (Statistics)
- Learning Outcomes
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On successful completion of this module, students will be able to:
- Derive the probability space for simple experiments, and prove simple properties of probabilities from its definition;
- Identify when random variables are independent, and derive conditional distirbutions and expectations;
- Define the most common discrete and continuous random variables and compute their moments and probabilities, moment and characteristic generating functions where appropriate;
- Define a multivariate distribution and calculate marginal and conditional distributions from it;
- State and prove the laws of averages and of central limit;
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- Module Content
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- Events and Probabilities;
- The laws of probability;
- Independence and conditional probability;
- Discrete random variables;
- Continuous random variables;
- Multivariate distributions & independence;
- Moment and characteristic generating functions;
- The law of averages and the central limit theorem;
- Examples and past exam questions;
- Module Prerequisite
- None
- Bibliography
- Probability: An Introduction by Grimmett and Welsh, published by Oxford University Press
- Introduction to Probability Models by Ross, published by Academic Press (10th edition)
- Assessment Detail
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This module will be examined jointly with ST2352
in a 3-hour examination in Trinity term,
except that those taking just one of the
two modules will have a 2 hour examination.