Example of Extinction Problem
Consider a parent can produce at most two offspring and the probabilities for the number produced are p0=.1, p1=.6, and p2=.3. The extinction probability in each generation is
- .
with d0=0. Here, the extinction probability is calculated from generation 1 to generation 20. The result is shown in the table.
For the ultimate extinction probability, we need to find d which satisfies d=p0+p1d+p2d2. In this example, d=1/3. This is exactly what the probabilities in the table converges to.
Read more about this topic: Branching Process
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