IE230 Chapter 2 Notes.docx

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Industrial Engineering
IE 23000
Andrew Liu

IE230 Notes 2.1.1 Random Experiments • Day-to-day repetitions can vary slightly due to small variations outside control o Said to have a random component o An experiment that can result in different outcomes, even though it is repeated in the same manner every time, it is called a random experiment 2.1.2 Sample Spaces • The set of all possible outcomes of a random experiment is called the sample space. The sample space is denoted as S. o Discrete sample space consists of a finite or countable infinite set of outcomes o Continuous sample space contains an interval of real numbers 2.1.3 Events • An event is a subset of the sample space of a random experiment o Union of two events is the event that consists of all outcomes in either E1UE2 o Intersection of two events is the even that consists of all outcomes in both events o Complement of an event is the set of outcomes that are not in the event E prime o Two events denoted as E1 and E2, such that E1 or E2 = empty set are said to be mutually exclusive 2.2 Interpretations and Axioms of Probability • Probability is used to quantify the likelihood that an outcome of a random experiment will occur • Whenever a sample space consists of N possible outcomes that are equally likely, the probability of each outcome is 1/N • For a discrete sample space, the probability of an event E1 denoted as P(E), equals the sum of the probabilities of the outcomes in E. • Probability is a number that is assigned to each member of a collection of events from a random experiment that satisfies the following properties: o If S is the sample space and E is any ev
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