Kumara Sastry wrote in message <[EMAIL PROTECTED]>...
>Suppose, X ~ Binomial(n1,p1), Y~Binomial(n2,p2) , and X and Y are
>independent. Also, Z = X+Y. Can anyone please comment on what the pdf
>of Z is?
>
>Thanks
>Kumara
>
Pr(Z=z) = Sum from l to u of p1(r).p2(z-r)
where p1 is the first binomial probability, and p2 is the second.
The upper & lower limits of summation, l & u, are not necessarily
0 and z but:
l = max(0, z-n2) and u = min(z, n1)
I hope I have got that right.
I doubt if the sum simplifies much.
--
Alan Miller, Retired Scientist (Statistician)
CSIRO Mathematical & Information Sciences
Alan.Miller -at- vic.cmis.csiro.au
http://www.ozemail.com.au/~milleraj
http://users.bigpond.net.au/amiller/
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