A single cell can either die, with probability .1, or split into two cells, with

Chapter 3, Problem 3.8

(choose chapter or problem)

A single cell can either die, with probability .1, or split into two cells, with probability .9, producing a new generation of cells. Each cell in the new generation dies or splits into two cells independently with the same probabilities as the initial cell. Find the probability distribution for the number of cells in the next generation.

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