I have two independent variables $X\sim \mathcal B(n,p)$, Binomial and $Y\sim \mathcal P(\lambda)$, Poisson. How would I go about finding the distribution of $Z=XY$ and the couple $(Z,S)$, where $S=X+Y$?
Product of two independent stochastic variables $XY$
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probability
probability-theory
probability-distributions
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0Is that binomial and Poisson? – 2012-11-07
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0@Jean-Sébastien yeah! I thought that was kind of obvious. I'm gonna add it. – 2012-11-07
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0I think it is obvious, but there isn't really a standard notation so who knows – 2012-11-07
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0Do you have any reason to believe that anything fancy can come out of it? – 2012-11-07
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0@did Yes because, I'm studying for an exam and I encountered it in a past question paper which made me believe that the Prof was looking for something "fancy". – 2012-11-07
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0I doubt there is. Even the distribution of $S$ alone is awkward. – 2012-11-07
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0@did but If I was to write the expression for $P(XY)$, how do I write it. I know $P(X+Y=k)= \sum P(X=i, Y=k-i)=\sum P(X=i) P(Y=k-i)$. – 2012-11-08
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0See Edit. $ $ $ $ – 2012-11-09