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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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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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