Derivation of Galton-Watson Process

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We derive the Galton-Watson branching process for the time-dependent extinction probability of a family name.
  1. Eric Eager
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Since f(t) is discrete, I think it's a "probability generating function", not a "moment generating function". If you differentiate and evaluate at 1, you will get the first moment, but the second derivative evaluated at 1 is the "factorial moment" E(X(X-1)), and so on for higher derivatives.

MichaelKohn-vz