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Unformatted text preview: done by applying a function to a random variable
that is uniformly distributed on the interval [0, 1]. The method is basically to use Example 3.8.11
in reverse–if applying FX to X produces a uniformly distributed random variable, apply F −1 to
a uniform random variable should produce a random variable with CDF F. Let F be a function
satisfying the three properties required of a CDF, as described in Proposition 3.1.5, and let U be
uniformly distributed over the interval [0, 1]. The problem is to ﬁnd a function g so that F is the
CDF of g (U ). An appropriate function g is given by the inverse function of F . Although F may
not be strictly increasing, a suitable version of F −1 always exists, deﬁned for 0 < u < 1 by
F −1 (u) = min{c : F (c) ≥ u}. (3.7) If the graphs of F and F −1 are closed up by adding vertical lines at jump points, then the graphs
are reﬂections of each other about the line through the origin of slope one, as illustrated in Figure
3.22. It is not hard to check that for an...
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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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