Consider a branching process with offspring distribution {bk}k> 0 and assume 0 < bo < 1. suppose the evolution is altered as follows. start with xo = 1, a single individual. if the next generation is not empty (that is, if x1 > 0), they invite an immigrant to join them (that is, x1 is replaced by x1 + 1). after that the evolution continues according to the usual rule. in particular, no further immigration takes place. find the extinction probability î of this new process. express it in terms of bo and the original extinction probability a. do we have ô < a for all 0 < a < 1, in other words, does the immigrant strictly improve chances of survival for all values 0 < a < 1? is it possible that û