CHAPTER 7 crash

CHAPTER 7 crash - CHAPTER 7: PROBABILITY 7.1 Introduction 3...

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CHAPTER 7: PROBABILITY 7.1 Introduction 3 views of probability 1. Subjective-personalistic view  2. Classical or logical view 3. Empirical relative-frequency view Probability theory provides a set of tools for dealing with situations involving uncertainty and the  foundation for statistical inference (2 nd  half of book) Subjective-Personalistic View of Probability Subjective-personalistic view –  probability is a measure of the strength of one’s expectation  that an event will occur Affect our lives because they enter into our decision making process Difficulties in incorporating it into a formal decision-making process because equally  knowledgeable individuals may disagree on the probability that an event will occur Cannot be considered apart from the person holding it Bayesian inference  – enables researchers to make decisions about some true state of affairs  using not only sample data but also any prior information that is available, either from previous  samples or in the form of informed opinions or beliefs The Classical, or Logical, View of Probability Classical  or  logical view  – probability of an event, say, A, is given by the number of events  favoring A, denoted by  n A ,   divided by the total number of equally likely events,  n S . Thus,  p (A) =  n / n S . Value of p(A) is between 0 and 1 inclusive since the number of events favoring A can never  exceed the total number of events— n ≤ n S . Based on logical analysis
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Experience has demonstrated that the classical view generates probability estimates that  closely approximate empirical probabilities. Classical view of probability is useful for practical problems. The Empirical Relative-Frequency View of Probability Use for experiments that can be repeated without changing their characteristics, such as coin  tossing and die rolling Probability is estimated from experience—by performing an experiment and determining the  ratio of the number of events of interest to the total number of events Empirical relative-frequency view  – the probability of event A, p(A), is a number approached  by the ratio n A /n  as the total number of observations, n, approaches infinity. As n gets larger and larger, you assume that the sample estimate n
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CHAPTER 7 crash - CHAPTER 7: PROBABILITY 7.1 Introduction 3...

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