Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | STATISTICAL THEORY AND METHODS II | ||
Code | MATH264 | ||
Coordinator |
Dr R Tatar Mathematical Sciences Radu.Tatar@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2016-17 | Level 5 FHEQ | Second Semester | 15 |
Aims |
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To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory. |
Learning Outcomes |
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After completing the module students should understand basic probability calculus. They should be familiar with a range of techniques for solving real life problems of the probabilistic nature. |
Syllabus |
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1 |
1 1. Events, probabilities, random variables, distribution functions, probability density functions, discrete and continuous random variables, independence. Mean, variance and moments of random variables. Functions of a random variable. Some commonly used distributions: Binomial and Negative Binomial, Weibull, Normal, Log-Normal Normal, Gamma distributions. Special distributions in statistics: Chi-squared, t, F distributions. 2. Multivariate random variables: Joint, marginal and conditional distribution functions, Conditional expectations. Covariance of random variables. Bivariate Normal distribution and independence of bivariate Gaussian random variables. 3. Transformations of random variables: Use of direct methods and generating functions. Sum and ratio of two random variables. 4. Gen erating functions: moment and probability generating functions. Central limit theorem. Approximations. As illustrations of motivation by practical examples: Chi-squared etc. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH101; MATH103; MATH162 |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
MATH366; MATH362; MATH481; MATH360; MATH361; MATH371; MATH374; MATH375; MATH480; MATH482; MATH483 |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme:GG13 Year:2 Programme:NG31 Year:2 Programme:G1N3 Year:2 |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Programme:G100 Year:2 Programme:G101 Year:2 Programme:G110 Year:2 Programme:G1N2 Year:2 Programme:G1R9 Year:2 Programme:G1X3 Year:2 Programme:GL11 Year:2 Programme:GN11 Year:2 Programme:GR11 Year:2 |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Written Exam | 2.5 hours | Second semester | 90 | Standard University Policy | Assessment 2 Notes (applying to all assessments) 10% Continuous Assessment Full marks will be given for complete answers to FIVE questions. Only the best FIVE will be taken into account. | |
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Coursework | Second semester | 10 | None: exemption approved November 2007 | University Policy applies - see Department/School handbook for details. | Assessment 1 |