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Unit-1.pdf - PROBABILITY Sercan Gr Vienna University of...

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PROBABILITY Sercan Gür Vienna University of Economics and Business Department of Statistics and Mathematics WU Vienna,12 March 2015

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Course Information Title: Probability (5239) Instructor: M.Sc. Sercan Gür Contact details: [email protected] Literature - John A. Rice, Mathematical Statistics and Data Analysis, 3rd Edition, Thomson Brooks/Cole, 2007. - Murray R Spiegel, John J. Schiller, R.Alu Sriniyasan, Schaum’s Outlines of Probability and Statistics, 2nd Edition, McGraw-Hill, 2000. Assessment %60 Written weekly exams (best 4 of 5 exams) %40 Final exam (tbd) %10 Class contributions 2/31
Course Information Lecture Hours: Day Hour Place Do, 12.03.2015 10:00-12:00 Uhr TC.3.08 Do, 19.03.2015 10:00-12:00 Uhr TC.3.08 Do, 26.03.2015 10:00-12:00 Uhr TC.3.08 Do, 16.03.2015 10:00-12:00 Uhr TC.3.08 Do, 23.04.2015 10:00-12:00 Uhr TC.3.08 Do, 30.04.2015 10:00-12:00 Uhr TC.3.08 Do, 07.05.2015 10:00-12:00 Uhr TC.3.08 Do, 21.05.2015 10:00-12:00 Uhr TC.3.08 Do, 28.05.2015 10:00-12:00 Uhr D1.1.074 Do, 11.06.2015 10:00-12:00 Uhr TC.3.08 Do, 18.06.2015 10:00-12:00 Uhr TC.3.08 Do, 25.06.2015 10:00-12:00 Uhr TC.3.08 3/31

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Course Content(Tentative) 1 Sample spaces, probability measures, computing probabilities. 2 Conditional probability, independence. 3 Exam 1. Discrete random variables: Bernoulli random variables, binomial distribution, geometric and negative binomial distributions, hypergeometric distribution, Poisson distribution. 4 Continuous random variables: Exponential density, gamma density, normal distribution. Functions of a random variable 5 Exam2. Joint distributions: Discrete random variables, continuous random variables. Independent random variables. 6 Conditional distributions, functions of jointly distributed random variables. 7 Exam 3. Expected values, variance and standard deviation, covariance and correlation. 8 Conditional expectation, moment-generating function. 9 Exam 4. The law of large numbers, convergence in distribution 10 Central limit theorem 11 Exam 5. Review 12 Final Exam 4/31
Part 1 Probability 5/31

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1 Introduction 2 Sample Spaces 3 Probability Measure 6/31
Probability Theory: Probability theory concerns with the analysis of random phenomena. Probability theory is essential to many disciplines (eg., finance, economics, engineering,...) Objective of this course is to cover basics of probability theory: I Understanding and modeling of random phenomenon I Define, describe and work with the basic concepts in probability I Use methods and ideas from probability to solve simple real-world problems. 7/31

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1 Introduction 2 Sample Spaces 3 Probability Measure 8/31
Sample Spaces In the study of probability, any process of observation is referred to as an experiment . The results of an observation are called the outcomes of the experiment. An experiment is called a random experiment if its outcome cannot be predicted. Definition 2.1 (Sample Space) The set, Ω , of all possible outcomes of a particular experiment is called the sample space for the experiment.A generic element of Ω is denoted by ω .
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