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.