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I need the step-by-step solution for this question.

If X and Y are aleatory independent variables with a Poisson distribution whose parameters are $\lambda_1$ and $\lambda_2$, respectively. Show that the aleatory variable $W=X+Y$ has a Poisson distribution too.

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  • $\begingroup$ I was adding a long comment to your conditional expectation problem when it got deleted! $\endgroup$ – copper.hat Jun 19 '19 at 19:40
  • $\begingroup$ Sorry, I thought that maybe I had forgotten to put a detail. $\endgroup$ – user655901 Jun 19 '19 at 19:43
  • $\begingroup$ I didn't notice that was another same question. I understand now how to do it. $\endgroup$ – user655901 Jun 19 '19 at 19:51
  • $\begingroup$ @RebecaSilva I'm pleased about that. $\endgroup$ – callculus Jun 19 '19 at 19:54