SCHOOL OF ENGINEERING BUILT （工程学院建）.pdfVIP

SCHOOL OF ENGINEERING BUILT ENVIRONMENT Mathematics Probability and Probability Distributions 1. Introduction 2. Probability 3. Basic rules of probability 4. Complementary events 5. Addition Law for Compound Events: A or B 6. Multiplication Law for Compound Events: A and B 7. Bayes Theorem 8. Tree Diagrams 9. Problems on Probability 10. Probability Distributions 11. Discrete Probability Distributions 12. The Expected value and Variance of a Discrete Probability Distribution 13. The Binomial Distribution 14. The Poisson Distribution 15. Continuous Probability Distributions 16. The Normal Distribution 17. Using Statistical Tables to Calculate Normal Probabilities 18. Worked Examples on the Normal Distribution 19. Problems on the Standard Normal Distribution 20. Problems on the Normal Distribution (General) 1 Probability and Probability Distributions 1 Introduction In life there is no certainty about what will happen in the future but decisions still have to be taken. Therefore, decision processes must be able to deal with the problems of uncertainty. Uncertainty creates risk and this risk must be analysed. Both qualitative and quantitative techniques for modelling uncertainty exist. In many situations large amounts of numerical data is available which requires statistical techniques for analysis. Quantitative modelling of uncertainty uses a branch of mathematics called Probability. This chapter introduces the concepts of probability and probability distributions. The application of statistical methods is very extensive and is used in all branches of Science and Technology, Industry, Business, Finance, Economics, Sociology, Psychology, Education, Medicine etc. Examples of Scenarios Inv