Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.

Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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