5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. 5B An individual can be either susceptible or infected, the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. 5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.

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For the following Markov models: a) write down the transition matrix M; b) find the stationary probability
distribution on paper;
5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of
closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond.
5B An individual can be either susceptible or infected, the probability of infection for a susceptible
person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day.
5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild
type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005
of having a wild type offspring.
Transcribed Image Text:For the following Markov models: a) write down the transition matrix M; b) find the stationary probability distribution on paper; 5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. 5B An individual can be either susceptible or infected, the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. 5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.
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