The offspring distribution of a branching process {Z.: n = 1.2. ... } is geometric

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The offspring distribution of
a branching process
{Zn; n = 1, 2,...} is geometric
distribution with parameters
0.4. If (Z = 1 and G₁(s) be the
probability generating
functions of distribution of
the n-th generation; n=1,2,3..
Find (round off to three
decimal points)
(i)
G3(0)
G4(0)
G5(0)
(ii) the probability that the
time that the process first
goes into extinction is at the
fifth generation
Transcribed Image Text:The offspring distribution of a branching process {Zn; n = 1, 2,...} is geometric distribution with parameters 0.4. If (Z = 1 and G₁(s) be the probability generating functions of distribution of the n-th generation; n=1,2,3.. Find (round off to three decimal points) (i) G3(0) G4(0) G5(0) (ii) the probability that the time that the process first goes into extinction is at the fifth generation
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