(a) let {z0,z1,z2...} be a branching process with z0=1 (start with a single individual). let Y denote the family size distribution, such that E(Y) = µ. prove that E(zn) = µ^n (b) suppose the family...

(a) let {z0,z1,z2...} be a branching process with z0=1 (start with a single individual). let Y denote the family size distribution, such that E(Y) = µ. prove that E(zn) = µ^n
(b) suppose the family size follows a Geometric with p = 0.3. find the expected population size by generation n= 10.
(c) assume again {z0,z1,z2...} is a branching process with z0 = 1 (start with a single individual). let Y denote the family size distribution, Y ~ Geometric(1/4). find the probability that the process will eventually die out.