工程统计学Handout4.pdfVIP

Engineering Statistics （工程统计学） Handout #4: Basic probability Jiandong Wang jiandong@ College of Engineering, Peking University Outline Outline • Definition of probability: basic concepts and properties • Conditional probability （条件概率） • Two theorems – Theorem of Total Probability （全概率公式） – Bayes’ Theorem （贝叶斯公式） Key points ： • Principles of Theorem of Total Probability and Bayes’ Theorem • Difference between the mutually exclusive events and independent events Assignment #3: see the last slide, Deadline: Oct 28, 2013 References • Chapter 2 in Montgomery and Runger (2011) 2 Motivation Motivation • If all past, present and future values of a variable are known precisely, without any uncertainty, then the variable is called as deterministic （确定的）. • However, in most practical situation, we cannot predict variables exactly. Such variables are called stochastic or random （随机的）. The fundamental characteristic of a stochastic or random variable is the inability to precisely specify its values beforehand. 统计学使用概率论和数学的方法， 研究如何收集数据，对这种数据进 行分析，以对所研究的问题做出判 断—— 概率论是统计学的基础。 Although random variables evolve in an imprecise manner, their average properties exhibit considerable regularity. 3 Definition of probability：basic concepts Definition of probability：basic concepts • Random experiment （随机试验）is an experiment can result in different outcomes, even though it is replaced in the same manner every time, e.g., the toss of a fair