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4.1: Random Variables
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A random variable is a quantitative variable that assigns a number to each outcome in the sample space of a given random experiment. A random variable can be either discrete (having specific values) or continuous (any value in a continuous range). The use of random variables is most common in probability and statistics as they quantify outcomes of random occurrences.
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4.2: Analyzing Discrete Random Variables
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In this section, we discuss methods of describing and analyzing discrete random variables.
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4.3: Binomial Distributions
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In the present section, we consider probability distributions for which there are just two possible outcomes with fixed probabilities summing to one. These distributions are called binomial distributions.
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4.4: Continuous Probability Distributions
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This section introduces the ideas surrounding the probability distributions of continuous random variables.
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4.5: Common Continuous Probability Distributions
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In this section, we name and explore key properties of some of the most commonly used probability density functions in statistical work. We will end by examining how certain regions within our distributions can directly relate to other regions within our distributions using some basic geometric reasoning.
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4.6: Accumulation Functions And Area Measures in Normal Distributions
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We have discussed the relationship between the area of regions within a continuous random variable's probability distribution and the probability of occurrence in relation to that variable. We now focus on how to produce these left-region area measures on normal distributions using technology. Once we reasonably master these concepts in relation to normal distributions, similar ideas are used in t− and χ2− distributions, as well as many other specialized distributions.