# Poisson distribution and properties of probability [duplicate]

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.

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