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204 7.1%2c2%2c3 Continuous distributions

204 7.1%2c2%2c3 Continuous distributions - Chapter 7...

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Chapter 7 Continuous distributions 7.1 The Normal and Uniform Distributions Discrete sample spaces have a countable number of elements, i.e. experimental outcomes. Each possible outcome for a random variable value has a probability between 0 and 1. The sum of the probabilities of all possible outcomes equals 1. For example if a fair die is rolled the probability of rolling a five is 1/6. In contrast, continuous sample spaces and continuous random variables occur when we are recording observations on a continuous scale (e.g. length and weight). Since there are an infinite number of possible outcomes the probability of any particular outcome must be zero. This gives us the problem of how to describe probabilities for continuous distributions. Instead of determining the probability of a single value (which would be zero) we find the probability of an interval of values. The following example illustrates this for a particular distribution.

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204 7.1%2c2%2c3 Continuous distributions - Chapter 7...

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