|Module Name||Applied Probability II|
|ECTS Weighting||5 ECTS|
|Semester taught||Semester 2|
|Module Coordinator/s||Prof. Caroline Brophy|
Module Learning Outcomes
On successful completion of this module, students will be able to:
LO1. Derive confidence intervals and hypothesis tests for means and variances.
LO2. Derive prediction intervals for simple statistical models and explain
how they differ from confidence intervals.
LO3. Conduct and explain the outputs of hypothesis testing in regression
LO4. Define maximum likelihood estimates and how to compute them.
LO5. Implement a bootstrap to construct confidence intervals.
LO6. Construct a q-q plot and use simple transformations of data that can
make it more Normally distributed.
LO7. Construct a probability plot for any given distribution where its
distribution function is known.
LO8. Calculate the properties of multivariate distributions.
LO9. Derive marginal and conditional probabilities of the bivariate Normal
Recap: derivation of the confidence interval and tests of hypothesis for normal data;
the difference between a confidence interval and a prediction interval.
The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis.
Hypothesis testing for regression analysis.
The bootstrap approach to confidence intervals and tests of hypothesis.
Introduction to maximum likelihood estimation and computation.
The q-q plot and transforming data to make it more Gaussian.
Introduction to multivariate distributions.
Teaching and learning Methods
Lectures and laboratories.
|Assessment Component||Brief Description||Learning Outcomes Addressed||% of total||Week(s) set||Week(s) Due|
|Examination||Real-time exam (2hrs)||All||85||n/a||n/a|
|Continuous assessment||Four assessment sheets||All (to date of each sheet)||15||2, 4, 6, 8||3, 5, 7, 9|
Examination (2 hours, 100%)
Contact Hours and Indicative Student Workload
|Contact Hours (scheduled hours per student over full module), broken down by:||31 hours|
|Tutorial or seminar||0 hours|
|Independent study (outside scheduled contact hours), broken down by:||79 hours|
|Preparation for classes and review of material (including preparation for examination, if applicable)||65 hours|
|Completion of assessments (including examination, if applicable)||14 hours|
|Total Hours||110 hours|
Recommended Reading List
George Casella, Roger L. Berger, Statistical Inference, 2nd Edition
Douglas C. Montgomery, George C. Runger, Norma F. Hubele, Engineering Statistics,
Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Introduction to
Linear Regression Analysis, 5th Edition
Prerequisite modules: STU11002 and STU22004. Alternatively, STU12501, STU12502 and STU23501.