1
$\begingroup$

I have three independent random variables:

$X_i$~$Poisson(i)$, $i=1,2,3$

I have no clue how find the distribution of the sum if I multiply them by some positive constant, say like:

$S= \sum_iiX_i$

for $i=1,2,3$

Without the constants I can just sum up the parameters since they are independent, then S will be:

$S$~$Poisson(6)$

But with the constants out front of each X, I have no idea how to start.

$\endgroup$
5
  • $\begingroup$ These will no longer be poisson, see here. $\endgroup$
    – Mark Schultz-Wu
    Commented Oct 23, 2017 at 23:50
  • $\begingroup$ Right, so i'm after how to start the convolution. $\endgroup$
    – Travis
    Commented Oct 23, 2017 at 23:52
  • $\begingroup$ See here for the $a_1X_1+a_2X_2$ case $\endgroup$
    – Mark Schultz-Wu
    Commented Oct 23, 2017 at 23:52
  • $\begingroup$ so try with the MGF's? $\endgroup$
    – Travis
    Commented Oct 23, 2017 at 23:53
  • $\begingroup$ Seems like it. Stats.stackexchange talks about a similar problem here without any clear (to me) answers. $\endgroup$
    – Mark Schultz-Wu
    Commented Oct 23, 2017 at 23:57

0

Reset to default

You must log in to answer this question.