My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
October 16th, 2014, 04:55 AM   #1
Joined: Oct 2014
From: Quebec, Canada

Posts: 1
Thanks: 0

Marginal probability density functions (pdf)

I have a set of two related queries relating to marginal pdfs:

i.How to proceed finding the marginal pdfs of two independent gamma distributions (X1 and X2) with parameters (α1,β) and (α2,β) respectively, given the transformation: Y1=X1/(X1+X2) and Y2=X1+X2.

I am using the following gamma formula:

(Attachment/image 1 included)

Having written the joint pdf and having applied the Jacobean, I have reached the final stage of writing the expression for the marginal (Y1):

(Attachment/image 2 included)

but I cannot proceed further, obtaining the marginal pdf.

ii.Additionally, given the following transformations , Y1=X1/X2 and Y2=X2, I have written the expression for the marginal (Y2):

(Attachment/image 3 included)

How do I find this marginal pdf?

Any enlightening answers would be appreciated.
Attached Images
File Type: jpg 1.JPG (10.8 KB, 3 views)
File Type: jpg 2.JPG (14.5 KB, 1 views)
File Type: jpg 3.JPG (15.9 KB, 1 views)
QuebecRb is offline  

  My Math Forum > College Math Forum > Advanced Statistics

density, functions, marginal, pdf, probability

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
PDF - probability density functions fobbz Calculus 2 March 4th, 2013 07:48 PM
Help with probability density functions? alb41192 Advanced Statistics 1 November 23rd, 2012 03:15 PM
Probability Density Functions smbrown Advanced Statistics 8 November 11th, 2011 07:48 AM
marginal/conditional density/probability sheila Advanced Statistics 0 October 20th, 2011 05:17 AM
Theory of Probability: Density Functions staceyrenee Advanced Statistics 2 December 13th, 2010 11:07 AM

Copyright © 2019 My Math Forum. All rights reserved.