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Unformatted text preview: 2.2. CONTINUOUS DENSITY FUNCTIONS 63 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 E .8 Figure 2.14: Calculation of distribution function for Example 2.14. When referring to a continuous random variable X (say with a uniform density function), it is customary to say that “ X is uniformly distributed on the interval [ a, b ].” It is also customary to refer to the cumulative distribution function of X as the distribution function of X . Thus, the word “distribution” is being used in sev- eral different ways in the subject of probability. (Recall that it also has a meaning when discussing discrete random variables.) When referring to the cumulative dis- tribution function of a continuous random variable X , we will always use the word “cumulative” as a modifier, unless the use of another modifier, such as “normal” or “exponential,” makes it clear. Since the phrase “uniformly densitied on the interval [ a, b ]” is not acceptable English, we will have to say “uniformly distributed” instead.]” is not acceptable English, we will have to say “uniformly distributed” instead....
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- Spring '09