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Unformatted text preview: ass points in any ﬁnite interval, then FX is a piecewise constant
A random variable X is a continuous-type random variable if the CDF is the integral of a
c fX (u)du. FX (c) =
−∞ The function fX is called the probability density function. Continuous-type random variables are
the subject of the next section.
The relationship among CDFs, pmfs, and pdfs is summarized in Figure 3.5. Any random vari- CDF FX
(always exists) pdf f X
pmf p X
Often more (for continuous!type
random variables ) Figure 3.5: Ways to describe distributions of random variables
able X on an arbitrary probability space has a CDF FX . The D in “CDF” stands for “distribution.”
But in common usage, the response to the question “What is the distribution of X ?” is answered
by giving one or more of FX , pX , or fX , or possibly a transform of one of these, whichever is
most convenient. Any of these have equivalent information and specify the probability of all events
involving X alone, but in...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land