I understand how a poisson distribution works....I'm just confused on how Node A maps to B and C in a way that passes along the properties of the poisson distribution.
I received the following problem as an assignment and am struggling to understand how to approach problems of this style:
1) The random number of data packets N that arrive at Node A is a Poisson random variable with mean (lambda). Each packet arriving at A immediately is sent to either Node B with probability p or to Node C with probability q=1-p, independently from packet to packet. Let L denote the number of packets sent from Node A to Node B, and R denote the number of packets sent from Node A to Node C.
(a)Show that L is a Poisson random variable with mean (lambda)*p.
(b)Are L and R statistically independent?
---Any help is appreciated. Thanks.