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# INDUSTRIAL SYS SIMULA ESI 4523

UF

GPA 3.66

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This 3 page Class Notes was uploaded by Ms. Dorian Wiegand on Friday September 18, 2015. The Class Notes belongs to ESI 4523 at University of Florida taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/206805/esi-4523-university-of-florida in Industrial Engineering at University of Florida.

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Date Created: 09/18/15

By Lian Qi A Refresher on Probability and Statistics Appendix C Simulation with Arena 3 quot ed Appendix C A Refresher on Probability and Statistics Slide 1 of 27 Probability Basics Experiment activity with uncertain outcome Flip coins throw dice pick cards draw balls from urn Operate a real call center Number of calls Average customer hold time Number of customers getting busy sbnaw Simulate a call center same questions as above 39 Sample space complete list of all possible individual outcomes of an experiment Could be easy or hard to characterize Simulation with Arena 3rd ed Appendix C A Refresher on Probability and Statistics Slide 3 of 27 What We ll Do 39 Outline 39 Review of probability and statistics necessary to do and understand simulation Probability basic ideas terminology Random variables Sampling Statistical inference point estimation con dence intervals Simulation with Arena 3rd ed Appendix C A Refresher on Probability and Statistics Slide 2 of 27 Probability Basics cont d 39 Event a subset of the sample space Union intersection complementation operations 39 Probability of an event is the relative likelihood that it will occur when you do the experiment A real number between 0 and 1 inclusively Denote by PE PE 0 F etc Interpretation proportion oftime the event occurs in many independent repetitions replications of the experiment Simulation with Arena 3rd ed Appendix C A Refresher on Probability and Statistics Slide 4 of 27 Appendix C Handout 1 Probability Basics cont d Some properties of probabilities If S is the sample space then PS 1 Can have event E 8 with PE 1 If a is the empty event empty set then Pw 0 Can have event E 0 with PE 0 If EC is the complement of E then PEC 1 PE PEUFPEPF PEmF lf Eand F are mutually exclusive ie Em F a then PEU F PE PF If E is a subset of F ie the occurrence of E implies the occurrence of F then PE S PF If 01 02 are the individual outcomes in the sample space then ZPo 1 all i E 39 39 39 3 ed Appendix C A Refresher on Probability and Statistics Slide 5 of 27 Random Variables A random variable RV is a number whose value is determined by the outcome of an experiment Technically a function or mapping from the sample space to the real numbers but can usually define and work with a RV without going all the way back to the sample space Think RV is a number whose value we don t know for sure but we ll usually know something about what it can be or is likely to be Usually denoted as capital letters X Y W1 W2 etc Probabilistic behavior described by distribution function E Simulation withArena 3 ed Appendix C A Refresher on Probability and Statistics Slide 7 of 27 Probability Basics cont d IfE Conditional probability Knowing that an event F occurred might affect the probability that another event E also occurred Reduce the effective sample space from S to F then measure size of E relative to its overlap if any in F ratherthan relative to S Definition assuming PF 0 PE F E and Fare independent if PE n F PE PF Implies PEF PE and PFE PF ie knowing that one event occurs tells you nothing about the other PEmF PF and F are mutually exclusive are they independent 39 39 L quot 3 ed Appendix C A Refresher on Probability and Statistics Slide 6 of 27 Discrete vs Continuous RVs range Discrete can take on only certain separated values Number of possible values could be finite or infinite Continuous can take on any real value in some Number of possible values is always infinite Range could be bounded on both sides just one side or neither E Simulation with Arena 3 ed Appendix C A Refresher on Probability and Statistics Slide 8 of 27 Appendix C Handout 2

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