lecture7ccle - THE BINOMIAL DISTRIBUTION LECTURE 7 CHAPTER...

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THE BINOMIAL DISTRIBUTION LECTURE 7 - CHAPTER 3.4 (ESPECIALLY 3.4.2)
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A little background from 3.3.1in your text (optional) In 1963, Stanley Milgram began a series of experiments to estimate what proportion of people would willingly obey an authority and administer painful electrical shocks to a stranger. Milgram found that about 65% of people would obey the authority and give such shocks. Over the years, additional research suggested this number is approximately consistent across communities and time
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Bernoulli Random Variable Each person in Milgram’s experiment can be thought of as a trial. We label a person a success if he/she refuses to administer the worst shock. A person is labeled a failure if he/she administers the worst shock. Because only 35% of individuals refused to administer the most severe shock, we denote the probability of a success with p = 0.35. The probability of a failure is sometimes denoted with q = 1- p. (so in this example q=0.65) Thus, success or failure is recorded for each person in the study. When an individual trial only has two possible outcomes, it is called a Bernoulli random variable.
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Properties of a Bernoulli Random Variable A Bernoulli random variable has exactly two possible outcomes. We arbitrarily label one of these outcomes a “success” and the other outcome a “failure”. In practice, when collecting these outcomes as data , we code “success” with a 1 and “failure” with a 0.
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Features of a 1,0 variable A one-zero (1,0) variable has nice mathematical properties. Suppose I were to randomly sample 10 of you to see if you were willing to administer a painful electrical shock to a total stranger. And suppose this was the result: 1, 0, 0, 1, 0, 0, 0, 0, 1, 0 We could write that 7/10 or .70 or 70% would or that 30% of you would not.
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Features of a 1,0 variable Mathematically, we could write this as And because 0 and 1 are numerical outcomes, we
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