In general, if A~Po(a) and B~Po(b) are independent random variables, then C = (A+B)~Po(a+b). Can someone please explain the intuition/simple proof of this and a word problem or example would really help to reinforce this concept. Thanks.
Hey gokuls and welcome to the forum.
Hint: Find the MGF of a Poisson distribution. What does it mean to calculate the MGF of A + B if A and B are independent variables? What is the form of the product of the two MGF's? What does this say about the distribution?