Question:

For the following Markov models a) draw the transition diagram, if one is not provided; b) put the states in (some) order and write down the transition matrix; c) calculate the probability of the given strings of states, taking the first state as given (e.g. for a string of 3 states, there are only 2 transitions.)

Use the transition diagram in figure a (Model 1) to calculate the probability of the string of states BAB.

Use the transition diagram in figure b (Model 2) to calculate the probability of the string of states CCD.

Use the transition diagram in figure c (Model 3) to calculate the probability of the string of states EEF.

Use the transition diagram in figure d (Model 4) to calculate the probability of the string of states GGG.

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.

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.

The genotype of 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: WWWW.

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.

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.

(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.

(Challenging) Now do the same for a sequence of Bernoulli trials where success has probability 0.9 (and failure has probability 0.1).

(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?

6 Question 8 (2 points) Suppose that we are performing a two-tailed test and compute a t-statistic of 0.181. If the sample size is 18, what is the P(t)? Use the provided t table in the Module to aid you in answering the question.The probability of committing a Type | error is: the level of significance always less than the probability of a Type II error 1.00 minus the probability of committing a Type II error equal to the standard error usually equal to the level of measurement Question 25 1 pts Which of the following probabilities indicates a relationship that is not statistically significant? 1001 01 Cart tell because statistical significance dependWhat is the definition of an observed p-value? O The probability that you observe your test statistic or one that is more extreme given the alternative hypothesis is true. O The probability that you observe your test statistic or one that is less extreme given the null hypothesis is true. O The probability that you observe your test statistic or one that is more extreme given the null hypothesis is incorrect. Magic O The probability of success observed in the population. O The probability that you observe your test statistic or one that is more extreme given the null hypothesis is true. O The probability of success observed in your sample.QUESTION 19 The says that when many people are insured. the probability distribution of the losses will assume a normal probability distribution. 0 probability distribution theorm 0 law of large numbers 0 skewed normal statistic 0 universal probability theorm QUESTION 20 Health insurance companies attempt to reduce costs by . O A. using group policies 0 C. encouraging insured persons to use the ER 0 C. attempting to shift costs to the employer 0 Both A. and C