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Unformatted text preview: state from any other state (ignoring edge directions) that has more than one equilibrium distribution. 5. Population dynamics can often be modeled by composing polynomials, and in this problem we will explore this possibility: suppose that you have a population of bacteria whereby from one generation to the next, a single individual will produce j ospring with probability p j , and that that individual dies in the next generation. Let f ( x ) = s j =0 p j x j . 1 Say that in our case f ( x ) = 1 / 2 + 1 / 4 x + 1 / 4 x 2 . If at time 0 the population has 1 individual, determine the expected number of individuals for when time t = 4. Hint: think about what f ( f ( x )) means, and then f ( f ( f ( x ))), etc. 2...
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 Spring '08
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 Statistics, Probability

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