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1. Two players match pennies and have between them a total of 5 pennies. If at any time one player has all of the pennies, to keep the game going, he gives one back to the other player and the game will continue. Show that this game can be formulated as an ergodic chain. Study this chain using the program ErgodicChain.
2. Calculate the reverse transition matrix for the Land of Oz example (Exam- ple 11.1). Is this chain reversible?
3. Give an example of a three-state ergodic Markov chain that is not reversible.
4. Let P be the transition matrix of an ergodic Markov chain and P∗ the reverse transition matrix. Show that they have the same fixed probability vector w.
suppose that you work for the child social services agency in your county. your job is to investigate instances of
State the alternative hypothesis that would be used to determine if Brand A has a higher proportion of defective smoke detectors than Brand B. Calculate the test statistic for determining if a difference exists between the failure rates of the two..
calibration of a glass electrode gave a reading of 145.7 mv with 0.05 m potassium hydrogen phthalate buffer standard ph
trials are performed in sequence. if the last two trials were successes then the next trial is a success with
A study determined that 5% of children fewer than 18 years of age live with their father only. Find the probability that at least 3 persons selected at random from 10 children less than 18 years of age lived with their father only.
Individual scores of a placement examination are normally distributed with a mean of 84.2 and a standard deviation of 12.8.
Dr. Walker is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress.
In a study that examines the effect of a peer mentor on the heart rate of patients, what is the dependent variable
for the following hypothesis test ho u lt 45 ha u gt 45 alpha 0.02. with n 80 ? 9 and 47.1 state the calculated
Conduct post hoc comparisons with the LSD method. Which groups differ significantly at α = 0.05?
In the researcher's sample of 1,500 children, the sample proportion of children was 0.0721. Compute the z-statistic of this sample proportion
if a relationship exists such that the more religiously involved one is the higher actual self-esteem is would you
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