MathDB

Assume that the number of offspring for every man can be

0,1,\ldots, n

with with probabilities

p_0,p_1,\ldots,p_n

independently from each other, where

p_0+p_1+\cdots+p_n=1

and

p_n\neq 0

. (This is the so-called Galton-Watson process.) Which positive integer

n

and probabilities

p_0,p_1,\ldots,p_n

will maximize the probability that the offspring of a given man go extinct in exactly the tenth generation?

A. 832