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[tex]P(X=x, Y=y)=\frac{a^ye^{-2a}}{x!(y-x)!}[/tex] where [tex]x=0,1,2,...y[/tex] and [tex]y=0,1,2...\infty[/tex], and [tex]a>0[/tex]

Find [tex]P(X=x)[/tex] and [tex]P(Y=y)[/tex]

An example is provided in a book on books.google.com

Page 96

http://books.google.com.au/books?id...AEwCTgK#v=onepage&q=marginal discrete&f=false

Here is my attempted solution

[tex]p_{X}(x)=\Sigma_{y=0}^{\infty}\frac{a^ye^{-2a}}{x!(y-x)!}=e^{-2a}+ae^{-2a}+\frac{a^2e^{-2a}}{x!(2-x)!}+...+\frac{a^ne^{-2a}}{x!(n-x)!}[/tex]

And then I cannot simplify this serie. Any comments and suggestions will be very much appreciated

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# Marginal distribution function

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