5. An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. Calculatethe probability of the ion channel going through the following sequence of states: COO.6. An individual can be either susceptible (S) or infected (I), the probability of infection for a susceptibleperson is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day.Calculate the probability of a person going through the following string of states: SISI.7. The genotypean organism can be either normal (wild type, W) or mutant (M). Each generation, awild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability0.005 of having a wild type offspring. Calculate the probability of a string of the following genotypesin successive generations: WWW.8. There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) . Every year,25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% oftrees are converted to shrubs, and 1% of trees are converted to grass; the other transitionprobabilities are 0. Calculate the probability of a plot of land have the following succession ofvegetation from year to year: GSGG.9. The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), andopen (O) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R),0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Calculate theprobability of the following string of states: OCCR.10. (Challenging) We considered a sequence of Bernoulli trials in chapter 4, for example a string of cointosses where each time heads and tails come up with probability 0.5. Describe this experiment as aMarkov model, draw its transition diagram and write its transition matrix.11. (Challenging) Now do the same for a sequence of Bernoulli trials where success has probability 0.9(and failure has probability 0.1).12. (Challenging) Can you formulate a test, based on a transition matrix of a Markov model, to tellwhether it's generating a string of independent random variables as opposed to a string of randomvariables that depend on the previous one?

Name: 5. An ion channel can be in either open (O) or closed (C) states. If
Uploaded: 2024-03-20T07:06:41.000Z
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Description: 5. An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. Calculatethe probability of the ion channel going

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5. An ion channel can be in either open (O) or closed (C) states. 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. Calculate the probability of the ion channel going through the following sequence of states: COO.