Question: 5. Let (Zn)n be a branching process with offspring distribution a. (a) (2pts.) If a = (0.5, 0.3, 0, 0.1, 0.1) then the process is

5. Let (Zn)n be a branching process with offspring distribution a. (a) (2pts.) If a = (0.5, 0.3, 0, 0.1, 0.1) then the process is subcritical/ critical/supercritical (underline the correct answer) (b) (2pts.) If a = (1/8, 3/8, 4/8) then the extinction probability of the process is . .... . (c) (2pts. ) If a = (1/3, 2/3) then P(Z2 = 1) =. ..... . . . . (d) (2pts.) If a = (1/2, 0, 1/2) then the probability that the process goes extinct by the second generation is

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