Density of continuous random variables?

Click For Summary
SUMMARY

The discussion focuses on finding the density functions for transformed random variables based on the given density function of an absolutely continuous random variable X. The density function fX(x) is defined as (3x^2-1)/12 for 1 PREREQUISITES

  • Understanding of probability density functions (PDFs)
  • Knowledge of transformation techniques in probability
  • Familiarity with continuous random variables
  • Basic calculus skills for function manipulation
NEXT STEPS
  • Study the method of transformation of random variables in probability theory
  • Learn about the Jacobian method for finding densities of transformed variables
  • Explore examples of density functions for common transformations
  • Review the properties of absolutely continuous random variables
USEFUL FOR

This discussion is beneficial for students in statistics or probability courses, educators teaching random variable transformations, and anyone involved in statistical analysis or data science requiring a solid understanding of density functions.

icup007
Messages
2
Reaction score
0
Can you please help me find the density of the following functions?

The density of an absolutely continuous random variable X is:

fX(x) =
{ (3x^2-1)/12 if 1<x<2
{ 1/2 if 2<x<3
{ 0 elsewhere

Find the density of Y where Y = 4X-2
Find the density of M where M = (X-2)^2


Thank you!
 
Physics news on Phys.org

Similar threads

Graduate Probability Density Function: Converting Experimental Observations to PDF
  • · Replies 4 ·
Replies
4
Views
3K
MHB Distribution and Density functions of maximum of random variables
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad How to show these random variables are independent?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Statistical modeling and relationship between random variables
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Linear regression and random variables
  • · Replies 30 ·
2
Replies
30
Views
5K
Graduate Constructing PDFs for Max Likelihood Density Estimation Problem
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Sample space, outcome, event, random variable, probability...
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Sampling theory and random sample
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Find P(X+Y>1/2) for given joint density function
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Karhunen–Loève theorem expansion random variables
  • · Replies 1 ·
Replies
1
Views
2K