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1. Explain why {Xn, n ≥ 0} is a branching process with X0 = 1 and the offspring
distribution:
f0 = 1/12, f1 = 2/3, f2 = 1/4.
2. Calculate the probability of the event that there are no red cells at time 2.5.
3. Find the expected number of red cells n minutes after the culture began and the
probability that the culture eventually dies out.
4. Suppose that, at time 0, a blood culture produces red cells according to a Poisson
distribution with mean λ = 2 rather than just one red cell (other facts related to
this question do not change). Find the expected number of red cells n minutes after
the culture began and the probability that the culture eventually dies out.