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# Module Descriptor School of Computer Science and Statistics

 Module Code ST2004 Module Name APPLIED PROBABILITY I Module Short Title ECTS 5 Semester Taught Michaelmas Contact Hours Lecture hours: 27, Lab hours: 5, Total hours: 33 Module Personnel Dr. Bernardo Nipoti Learning Outcomes Students will have the ability: to analyse problems by means of a Monte Carlo approach to formalise and solve probability problems to use the language of random variables, their expected values and their probability distributions to use conditional distributions to deal with special families of probability distribution to understand the concepts involved in simple and linear regression analysis Learning Aims In this course we will first take a problem-based approach that replaces mathematics with the use of random numbers in a spreadsheet, by following what is known as the Monte Carlo method. This approach will allow students to rapidly acquire the facility to model complex random systems. We will subsequently learn the language of probability which can sometimes by-pass the algorithms, or render them more efficient. We introduce the formal language of probability theory, we will get familiar with special families of probability distributions and investigate their properties. Finally we will introduce the notions of simple linear regression. Module Content Specific topics addressed in this module include: Monte Carlo approach Empirical Law of Large Numbers  True and pseudo random number generation Generation of random permutations Frequentist probability Axiomatic foundations of probability Derivation of basic rules of probability from axioms Independence of events Conditional probability Law of conditional probability Bayes theorem Random variables and their distributions Expectation and its properties Independent random variables Transformations of random variables Special families of discrete and continuous distributions Connection between distributions Markov inequality and Chebyschev inequality Joint probability mass function, Marginal distributions Covariance and correlation Simple linear regression model Recommended Reading List Main text: Tijms, “Understanding Probability”, Cambridge 2012. Additional material will be provided when needed. Module Prerequisites Elementary mathematics including integration. Assessment Details Exam (80%), one compulsory group project (20%) Supplemental: 100% Exam Module Website Academic Year of Data 2017/18