Let F : ( [0, 1] be non-decreasing, right continuous, F(- () = 0 and F(()
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F-1 (y) = inf {x ( (; F(x) ( y}, y ( [0, 1].
Next, consider the probability space ((, A, P) = ([0, 1], B[0, 1], P), where P = ( is the Lebesgue measure, and on (, define the function X by X (() = F-1((). Then show that X is a r.v. and that its d.f. is F.
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Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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