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Digital Dice by Paul J. Nahin

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21. Chain Reactions, branching processes, and Baby Boys

Before getting to the writing of a simulation code to estimate the answers to the questions posed in the original problem statement, let me show you a beautiful theoretical solution. I’ll then use this solution to validate the code. If we have {pi} as the sequence of probabilities that a man will have i sons, i ≥ 1, then define the so-called generating function of this sequence to be

 

f(x) = p0 + p1x + p2x2 + p3x3 + . . .

where there is no physical significance to x. What Hawkins and Ulam ...

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