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# Find PDF from Negative Binomial Distribution HELP!?

If X~NB(r,p) then find the PDF of Y = X - r.

The answer is:

[ (y+r-1) , (r-1) ] p^r(q)^y ; y=0,1,2,...

I have no idea how to get to that. Any help would be appreciated.

### 1 Answer

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- JackLv 49 years agoFavorite Answer
x=w(y) = y+r

dw(y) / dy = 1

The PDF for a negative binomial is [ (x-1) , (r-1) ] p^r q^x-r

Thus, the formula for the pdf of y is fx(y+r) |dw(y)/dy|

So the second part is 1, so that just disappears. Finally, in the first part, all you need to is plug in y +r wherever you see x.

Thus, you get: [ (y+r-1) , (r-1) ] p^r(q)^y

Hope that helps!

Source(s): BAM!

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