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Content

Content The tentative topics for this course include: • Review of Probabillity, Random variables, Distributions, Conditioning and Expectations • Approximations to expected values and variances • Central Limit Theorem and Law of Large Numbers • Methods for finding estimators: Point estimation, fitting probability distributions, Maximum likelihood estimation • Methods of evaluating estimators: Mean Squared Error, Best Unbiased estimators; sufficiency and unbiasedness. • Large Sample theory and Confidence Intervals • Hypothesis Testing , Neyman-Pearson Paradigm, Uniformly Most Powerful Tests • Generalized Likelihood ratio tests, tests for normality and Bootstrap • Large Sample Methods: Rank Tests; Experimental Design issues. • Application to analysis of categorical data; Logistic regression • Validation of predictive models; bootstrap; Jackknifing and cross-validation • Bayesian Methods

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Conditions of Participation

There are no prerequisites for this course . Knowledge of basic mathematics would suffice as the course is taught in such a manner that the material is understood by all. Knowledge of basic probability and statistics, and linear algebra, such as knowledge of the probability distributions and elementary hypothesis testing may be an asset.

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Teaching Methods

• Lectures will provide valuable synthesis and evaluation of the growing body of available information, update current issues and events, and prioritise content relevant to course assessment. • Every week practical sessions will provide hands-on experience for students to gain skills required for solving basic statistical problems. Once basic competency is mastered, they will be introduced to more automated methods using statistical software. • The online teaching tool, myeLearning, will be used during this course for communication among students and staff for official posting of important notices and provision of recommended resource materials and links to resources on specific websites.

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Learning outcomes / Competences

At the end of this course, students should be able to: ● Use point estimation and interval estimation to estimate good values for population parameters. ● Use hypothesis testing to determine if there is evidence to support conclusions. ● Use techniques such as Cross-validation and Jacknife resampling to validate predictive models. ● Model prediction problems. ● Identify real-world applications.

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Forms of examination

Examinations are delivered online via the moodle platform (myelearning). Final examinations are asynchronous in nature and students are normally given 3 days to complete it. Coursework examinations are asynchronous in nature and normally completed within 2 days. Take-home assignments are also given. A typical breakdown of the assessment is: • Final Examination (50%) • Coursework Exams (40%) • Assignments (10%)

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Conditions for allocation of credit points

Students must pass both the coursework and the final examination

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Other information

This is an introductory course in Probability and Statistics. It is a mandatory course in the Master of Science in Data Science at the UWI. Literature Resources: Statistical Software (R programming language) which is freely available. Reading Material: Statistics; Informed Decisions Using Data plus MyStatLab with Pearson eText (5th ed) by Michael Sullivan Probability and Statistics 4th edition by Morris de Groot and Schervish; Addison-Wesley Mathematical Statistics with Applications, 7th Edition, Miller and Miller, Pearson