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## Chapter 11

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**Chapter 11**Understanding Randomness**Randomness**• Many phenomena in the world are random: • Nobody can guess the outcome before it happens. • When we want things to be fair, usually some underlying set of outcomes will be equally likely • Example: • Flip a fair coin. • Roll a die**Questions**• When we survey a small group of people, how do we know this sample is truly representative of the overall population? • How do insurance companies, casinos determine their profit even though the outcomes are truly random?**Why Be Random?**• The best ways we know to generate data that give a fair and accurate picture of the world rely on randomness, and the ways in which we draw conclusions from those data depend on the randomness, too.**It’s Not Easy Being Random**• It’s surprisingly difficult to generate random values even when they’re equally likely. • Computers have become a popular way to generate random numbers. • Even though they often do much better than humans, computers can’t generate truly random numbers either. • Since computers follow programs, the “random” numbers we get from computers are really pseudorandom. • Fortunately, pseudorandom values are good enough for most purposes.**A Simulation**• We need an imitation of a real process so we can manipulate and control it. We are going to simulate reality. • Simulations can provide us with useful insights about the real world. • We use Table of Random Digits to obtain simulated outcome. • A simulation model can help us investigate a question when we can’t (or don’t want to) collect data, and a mathematical answer is hard to calculate.**Homework Assignment**• Page 299 – 301 • Problem # 7, 9, 31.