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
Famous quotes containing the words extinction and/or problem:
“The problems of this world are only truly solved in two ways: by extinction or duplication.”
—Susan Sontag (b. 1933)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)