Let branching process with offspring distribution
p0 = .5 , p1 = .1 , p3 = .4 (extinction probability a = .7247)
and assume X0 = 1.
i) Find probability that population is extinct in second generation (X2 = 0), provided that it didn't die out in first generation (X1 > 0)?
ii) Find probability that population is extinct in third generation, provided that it was not extinct in second generation?