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1 Probability

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2 Probability has three related “meanings.” 1. Probability is a mathematical construct. Probability

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3 Probability has three related “meanings.” A consequence of the mathematical meaning: 2. If a probability is attached to an event, then the probability of an event is the long term (technically forever) relative frequency of occurrence of the event, when the experiment is performed repeatedly under identical starting conditions. Probability

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4 Random selection of a unit from a population: Each unit is equally likely to be the chosen unit. It is rare that one randomly selects a single unit from the population. However, the variable that conceptually results from such a selection has the same distribution as does the population. Random Selection

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5 Probability has three related “meanings.” 3. If there is random selection of one unit from a population, then the probability of an event is the relative frequency of units in the population for which the event applies. Probability

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6 Definitions of Probability 2. the probability of an event is the long term (technically forever) relative frequency of occurrence of the event, when the experiment is performed repeatedly under identical starting conditions. 3. The probability of an event is the relative frequency of units in the population for which the event applies. To aggregate these meanings: The probability associated with an event is its relative frequency of occurrence over all possible ways the phenomena can take place. Probability Models and Populations

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