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:
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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
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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