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October 16th, 2014, 04:55 AM   #1
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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)
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