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October 16th, 2014, 04:55 AM  #1 
Newbie 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. 

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density, functions, marginal, pdf, probability 
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