Branching Process - Example of Extinction Problem

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:

    “I wish all men to be free. I wish the material prosperity of the already free which I feel sure the extinction of slavery would bring.”
    —Abraham Lincoln (1809–1865)

    “A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be answered, moveover, in a word—‘Everything.’”
    —Willard Van Orman Quine (b. 1908)