- #1
_joey
- 44
- 0
Given:
[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
[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