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F78PB Probability and Statistics B Lecturer: George Streftaris Aims To reinforce basic ideas related to the description and analysis of data, and provide the basis for the application of statistical modelling, estimation, hypothesis testing and regression. Summary This course follows on from Probability and Statistics A. It develops the basic ideas used in statistical analysis and inference, with an emphasis on how we learn from data using both graphical techniques and statistical methodology based on probability theory. Topics presented include: analysis of simple data; construction of statistical models; sampling distributions and properties of estimators; method of moments and introduction to maximum likelihood estimation; inference for data from one population; comparisons of data from two populations; confidence intervals with samples from one or two populations; hypothesis testing; issues related to association between two variables; linear regression; statistical computing. Learning outcomes After studying this course, students should be able to: Understand, interpret and describe data using appropriate numerical and graphical summaries Understand issues related to data collection, model construction and model choice Calculate point estimates using the method of moments Understand the concept of maximum likelihood estimation and derive maximum likelihood estimates in various applications Compare data from two populations Construct, calculate and interpret confidence intervals for parameters of interest in one or two populations Understand and interpret the concepts of null hypothesis, alternative hypothesis, critical region, level of significance and P-values Perform hypothesis tests for population parameters Investigate associations between two variables Perform linear regression analysis and interpret findings meaningfully Demonstrate results related to sampling distributions, the central limit theorem and confidence intervals using simulation Reading J.E. Freund’s mathematical statistics, by I. Miller and M. Miller, 6th ed., Prentice-Hall, 1999. Assessment Two-hour written examination (80%); continuous assessment (20%) Feedback Feedback on submitted and assessed work will be provided at tutorial classes. Students can also obtain feedback from the lecturer during office hours. Help If you have any problems or questions regarding the course, you are encouraged to contact the lecturer. Course web page Further information and course materials will be available on Vision Detailed syllabus Analysis of simple data (single variable distributions) Construction of statistical models Sampling distributions, some properties of estimators Introduction to the method of moments and maximum likelihood Statistical inference for data from one population Comparisons of data from two populations Confidence intervals with samples from one or two populations Hypothesis Testing: introduction, terminology and test statistics for typical situations Issues related to association between two variables: graphical techniques, correlation and contingency tables Linear regression Statistical computing