Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
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...
See similar textbooks
icon
Related questions
Question

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. 

Expert Solution
Step 1

Consider X as a random variable with a continuous distribution function F.

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer