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Unformatted text preview: ass points in any ﬁnite interval, then FX is a piecewise constant
function.
A random variable X is a continuoustype random variable if the CDF is the integral of a
function:
c fX (u)du. FX (c) =
−∞ The function fX is called the probability density function. Continuoustype 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
(for discrete!type
random variables)
useful
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
 Zahrn
 The Land

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