Consider binary splitting, that is, the branching process where the distri- bution of Y = the number of children is given by (Y = 2) = 1 - P (Y = 0) = p, 0 < p=""> 1.
However, suppose that p is not known, that p is random, viz., consider the following setup: Assume that P (Y = 2 | P = p) = p, P (Y = 0 | P = p) = 1 - p, with (2x, for 0 x 1,fP (x) = 0, otherwise.
(a) Find the distribution of Y.
(b) Determine the probability of extinction.