Galton Watson branching process

[Lauren1231]

Using Galton Watson branching process. Assume that a fox had 0,1,2,3 offspring with probabilities p0,p1,p2,p3 respectively. find the probability distribution for G1 and G2.

below is what I’ve done so far I think this is correct for G1 however I’m unsure where to even start with G2.

 

[staassis]

You did not specify what G1 and G2 are. Anyway, distributional properties of branching processes are often derived with the help of moment generating functions (or characteristic functions). One tool to consider. Cannot say more without knowing the exact problem.

 

[Lauren1231]

this is all the information given to me except mines for 0-3 not 0-2

 

[staassis]

Great. So you see yourself that the course is encouraging you to use probability generating functions, which are equivalent to moment generating functions with substitution z = exp{t}.

 

[Lauren1231]

Right ok so is there a method to follow to obtain G2?