Question: . (12 points) A vial in a biochemistry lab has a population of genetically engineered micro-organisms called the HAPPY-Q. A scientist wishes to keep track

. (12 points) A vial in a biochemistry lab has a population of genetically engineered micro-organisms called the HAPPY-Q. A scientist wishes to keep track of the size of this population. A new HAPPY-Q individual can enter this population in three ways (i) each existing HAPPY-Q individual can split into two after an exponentially distributed amount of time with parameter A, (i1) the vial is connected by a tube to a population of HAPPY-X micro-organisms that can create one HAPPY-Q individual after an exponentially distributed amount of time with parameter A, and (ii1) the vial is also connected by a tube to a population of HAPPY-Y micro-organisms that can create one HAPPY-Q individual after an exponentially distributed amount of time with parameter 2. Each HAPPY-Q individual lives an exponentially distributed amount of time with parameter p. The scientist has added a population control chemical which does not allow the HAPPY-Q population to grow beyond four (i.e. the maximum population 1s four). a. (5 points) Model the number of HAPPY-Q in the vial as a birth-death process by drawing its rate diagram. Then suppose A=1, p=1. \f

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