Bernadelli studied a beetle which lives three years only. and propagates in as third

Chapter 5, Problem 5.3.2

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Bernadelli studied a beetle which lives three years only. and propagates in as third year. They survive the first year with probability 1 2 , and the second with probability 1 3 , and then produce six females on the way out: Beetle matrix A = 0 0 6 1 2 0 0 0 1 3 0 . Show that A 3 = I, and follow the distribution of 3000 beetles for six years.

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