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Unformatted text preview: 2.2. CONTINUOUS DENSITY FUNCTIONS 61 A glance at the graph of a density function tells us immediately which events of an experiment are more likely. Roughly speaking, we can say that where the density is large the events are more likely, and where it is small the events are less likely. In Example 2.4 the density function is largest at 1. Thus, given the two intervals [0 , a ] and [1 , 1 + a ], where a is a small positive real number, we see that X is more likely to take on a value in the second interval than in the first. Cumulative Distribution Functions of Continuous Random Variables We have seen that density functions are useful when considering continuous ran dom variables. There is another kind of function, closely related to these density functions, which is also of great importance. These functions are called cumulative distribution functions. Definition 2.2 Let X be a continuous realvalued random variable. Then the cumulative distribution function of X is defined by the equation...
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 Spring '09
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