Function of Function of Random variable

[gkannan16]

Homework Statement

Has anyone heard of function of function of random varibale. That is the pdf of a random variable is a function of another random variable. If yes can some give reference for the same.

Homework Equations

The Attempt at a Solution

 

[Defennder]

Yes there's such a thing. It's just called function of a random variable. A google search yields this:
http://www.colorado.edu/geography/courses/geog_4033_f05/lectures/RV%20functions.pdf

 

[Mene]

Yes, I am familiar with the concept of function of function of random variables. This refers to the idea that the probability density function (PDF) of one random variable can be expressed as a function of another random variable. This is known as a transformation of random variables and is a common technique in probability theory and statistics.

One example of this is the transformation from a normal distribution to a chi-squared distribution. In this case, the chi-squared distribution is the function of the squared standard normal distribution.

A good reference for this concept is the book "Probability and Statistics" by Morris H. DeGroot and Mark J. Schervish. Chapter 6 specifically covers transformations of random variables and their properties.