0
$\begingroup$

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 $S=X+Y$?

  • 0
    Is that binomial and Poisson?2012-11-07
  • 0
    @Jean-Sébastien yeah! I thought that was kind of obvious. I'm gonna add it.2012-11-07
  • 0
    I think it is obvious, but there isn't really a standard notation so who knows2012-11-07
  • 0
    Do you have any reason to believe that anything fancy can come out of it?2012-11-07
  • 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
  • 0
    I doubt there is. Even the distribution of $S$ alone is awkward.2012-11-07
  • 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
  • 0
    See Edit. $ $ $ $2012-11-09

1 Answers 1