Statistics
ST235: Probability (5 ECTS)
This is an introductory course to probability theory. Topics include: algebra of events, concepts of conditional probability and independence of events; random variables (rv); discrete and continuous propability distributions; expectation, variance and functions of rv-s; probability and moment generating functions; basic probability inequalities.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Apply basic laws of probability theory to calculate probabilities of composite events obtained by applying set operations
- Apply correct combinatorial random sampling rules and calculate probabilities
- Use basic properties of probability distributions to calculate derived quantities
- Calculate expectations, conditional expecations and variance of a variety of r.v.-s
- Prove main theorems and results connecting basic probaility concepts including joint and conditional rv-s
- Understand common properties and differences of discrete and continuous r.v.-s
- Calculate expectations, variances and distributions of functions of rv-s
- Apply generating functions to calculate corresponding distributional properties
Indicative Content
This is an introductory course to probability theory. Topics include: algebra of events, probability spaces, conditional probability, independence of events; cobinatorics and random sampling; concept of a random variable (rv); discrete and continuous probability distributions (mass, density and cumulative distribution functions); functions of rv-s; properties of expectation and variance; conditional and joint rv-s and probability distributions; probability and moment generating functions; Markov and Chebyshev inequalities; Weak law of large numbers; Central limit theorem.
Module Resources
1) C. Grinstead and L. Snell, Introduction to Probability, American Mathematical Society (free online copy)
2) Hoel, Port, Stone, Introduction to Probability Theory, Houghton & Mifflin
3) Stirzaker, Probability and Random Variables, Cambridge
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