Download AM20RA Real Analysis

AM20PD
Level: 5
PROBABILITY DISTRIBUTIONS
Credits: 10
Teaching Period: 2
Module Tutors: Dr J Van Mourik
Aims
Understand the general principles of probability distributions.

Be familiar with the properties of important probability distributions.

Encounter some applications of probability distributions in random processes.

Understand the Central Limit Theorem.
They should be able to:

Use probability distributions to calculate expectations.

Determine marginal and conditional distributions and (in)dependence from joint probability
distributions

Use moment generating functions to derive properties of probability distributions.

Apply the Central Limit Theorem.

Analyse a simple random process.
Content:
Probability distributions for discrete and continuous random variables, including:
Uniform, Bernoulli, Binomial, Poisson, Exponential, Normal, Gamma, Dirac
Delta,...
Joint probability distributions.
Moment generating functions.
The Central Limit Theorem and its applications
Random processes.
Teaching:
Lectures 22 hours
Tutorials 11 hours
Coursework, further study and examination 67 hours
Assessment: 1 Class Test (1 hour)
10% (week Date & Time TBC )
1 Course Work
10%
Examination (1.5 hours) 80% (Summer Examination)
Module outcomes
What the student should gain from successful completion of the
module
Knowledge and Understanding
1. Understand the underlying principles of probability and
random variables.
2. Know the important properties of probability distributions.
Intellectual Skills
1. Understand the underlying principles of probability and
random variables.
2. Know the important properties of probability distributions.
Professional/Subject-Specific Skills
1. Calculate expectation values for (joint) discrete and/or
continuous random variables, determine their
independence.
2. Derivation and use of the moment generating function for
random variables.
3. Central Limit Theorem and its applications.
4. Application of properties of probability distributions to
random processes.
Transferable Skills
1. Presentation, time management
SEAS, Aston University – AM Module Specification 2011/12
Teaching/Learnin
g
Methods
Assessment
Methods
Lectures/Tutorials
Examination/
Coursework
Lectures/Tutorials
Examination/
Coursework
Lectures/Tutorials
Examination/
Coursework
Lectures/Tutorials
Examination/
Coursework
Last update 05/09/11
Reading List: Grimmet, G., Stirzaker, D. (1992) Probability and Random Processes. 2nd Edition. OUP:
Oxford.
Lipschutz and Schiller (1998), Introduction to Probability and Statistics, Schaum’s outline
series, McGraw-Hill.
Stirzaker D. (1999), Probability and Random Variables: a Beginner's Guide, Cambridge UP.
Prerequisites: Transition Mathematics (AM10TM)
Statistics and Probability (AM10SP)
Introduction to Analysis (AM10IA)
Corequisites: Real Analysis (AM20RA)
Multi-variate Calculus Analysis (AM20MC)
SEAS, Aston University – AM Module Specification 2011/12
Last update 05/09/11