PSLS.PPT.Ch12

PSLS.PPT.Ch12 - Discreteprobability distributions PSLS...

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    Discrete probability  distributions PSLS chapter 12 © 2009 W.H. Freeman and Company
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Objectives (PSLS chapter 12) Discrete probability distributions The binomial setting and binomial distributions Binomial probabilities Binomial mean and standard deviation The Normal approximation to binomial distributions The Poisson distributions Poisson probabilities
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Reminder: the two types of data Quantitative Observations that can be counted or measured across individuals in the population (e.g., your height, your age, your IQ score). Categorical Observations that fall into one of several categories (e.g., your gender, your hair color, your blood type — A, B, AB, O ). How do you figure it out? Ask: What are the n individuals/units in the sample (of size “ n ”)? What is being recorded about those n individuals/units? Is that a number ( quantitative) or a statement ( categorical)?
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Binomial setting and distributions Binomial distributions are models for some categorical variables, typically representing the number of successes in a series of n independent trials. The observations must meet these requirements: the total number of observations n is fixed in advance each observation falls into just one of two categories: success and failure the outcomes of all n observations are statistically independent all n observations have the same probability of “success,” p.
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Applications for binomial distributions Binomial distributions describe the possible number of times that a particular event will occur in a sequence of observations. They are used when we want to know the probability of the number of times that an occurrence takes place. In a clinical trial, a patient’s condition may improve or not. We study the number of patients who improved, not how much better they feel. Is a person ambitious or not? The binomial distribution describes the number of ambitious persons, and not how ambitious they are. In quality control we assess the number of defective items in a lot of goods, irrespective of the type of defect.
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We express a binomial distribution for the count X of successes among n observations as a function of the parameters n and p : B ( n , p ). The parameter
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PSLS.PPT.Ch12 - Discreteprobability distributions PSLS...

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