In every generation of a dynasty the number of children born

In every generation of a dynasty, the number of children born is X iidpoisson ()For each child born, one can think of the event of them surviving to have children of their own is X iidbernulli(p) what is the distribution of the number of children one has that survive to have their own children? What is the distribution of the number of grandchildren one has?

Solution

what is the distribution of the number of children one has that survive to have their own children?

bernoulli, it is bernoulli because one can think of the event of them surviving to have children of their own

What is the distribution of the number of grandchildren one has?

poisson

it is poisson distribution because In every generation of a dynasty, the number of children born is a poiison distribution