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?

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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.

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.

MATLAB: An Introduction with Applications

6th Edition

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

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.
6. An individual can be either susceptible (S) or infected (I), 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.
Calculate the probability of a person going through the following string of states: SISI.
7. The genotype
an organism can be either normal (wild type, W) or mutant (M). 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. Calculate the probability of a string of the following genotypes
in 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% of
trees are converted to shrubs, and 1% of trees are converted to grass; the other transition
probabilities are 0. Calculate the probability of a plot of land have the following succession of
vegetation from year to year: GSGG.
9. The NACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and
open (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 the
probability of the following string of states: OCCR.
10. (Challenging) We considered a sequence of Bernoulli trials in chapter 4, for example a string of coin
tosses where each time heads and tails come up with probability 0.5. Describe this experiment as a
Markov 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 tell
whether it's generating a string of independent random variables as opposed to a string of random
variables that depend on the previous one?

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