Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
None Array 

Description MS117 aims to introduce the basic concepts of probability theory through a mixture of lectures, demonstrations and assignments in R and problem solving based tutorials. The module will give students a working knowledge of the main techniques of elementary probability and build a solid foundation for learning more advanced topics in probability and statistics. Students must pass both the continuous assessment and end of semester exam for this module in order to pass the module.  
Learning Outcomes 1. Define elementary concepts of probability and state the main theorems. 2. Use counting techniques to assign probabilities to events. 3. Compute and apply conditional probabilities 4. Derive the basic properties of common discrete and continuous distributions 5. Generate samples of random numbers from various distributions and investigate sample properties empirically in the R statistical computing language. 6. Derive the expectation and variance of important distributions and prove their theoretical properties  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
Revision of Probability Models and Combinatorics Basic definitions and axioms, general probability models with discrete and continuous sample spaces. Basic rules, ordered samples unordered samples, partitions. Conditional Probability Independence, law of total probability, Bayes theorem. Discrete Random Variables Definition, probability functions, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common discrete distributions. Continuous Random Variables Definition, probability density function, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common continuous distributions. Numerical Experiments in R Inverse transform method, the central limit theorem, definition of a sample, numerical investigations of theoretical results in R.  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes
 
Date of Last Revision  11MAY12  
Archives: 
