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Modeling Scenario

1-001s-StochasticMDeathImmigration-ModelingScenario

Author(s): Chris McCarthy

Keywords: simulation data logistic immigration stochastic death fitting

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Abstract

Resource Image We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

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Description

{The process}: We start each step by shaking our bag of mms.

We empty the bag onto a plate.

The m&ms that land with their m showing up are considered to have died and are removed from the plate.

The m&ms without the m showing are considered to have survived the step and are put back into the bag.

The step ends by our putting an additional 10 ``immigrating'' mms into the bag.

We assume that the probability that an mm will land with an m facing upwards is 1/2.

The question: What is the probability distribution for the number of m&ms that are alive at the end of the nth step and how many m&ms should we expect to be alive at the end of the nth step?

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Authors

Author(s): Chris McCarthy

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