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1. (Wheel of Fortune Continued). Consider again the Markov chains corresponding to the wheel of fortune. Prove or disprove that they are irreducible and aperiodic.
2. * (Stationary Distribution in Ehrenfest Model). Consider the general Ehrenfest chain defined in the text, with m balls, and transfer probabilities ?; ?; 0 ?; ? 1. Identify a stationary distribution if it exists.
3. * (Time Until Break away). Consider a general stationary Markov chain fXng, and let T D minfn > 1W Xn ¤ X0g.
(a) Can T be equal to 1 with a positive probability?
(b) Give a simple necessary and sufficient condition for P.T 1/ D 1.
(c) For the weather pattern, Ehrenfest urn, and the cat and mouse chain, compute E.T jX0 D i/ for a general i in the corresponding state space S.
compute a 95 confidence interval for the population mean based on the sample 1 2 3 4 5 6 and 39. change the number from
flaws in a certain type of drapery material appear on the average of three in 250 square feet. if we assume the poisson
In part b, the sample have greater variability than part a, but the sample sizes are unchanged. how does the larger variability affect the size of the standard error for the sample mean?
Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Disney tells you that the average distance between the ears on a Mickey Mouse hat is 5 inches. In a sample of 100 Mickey Mouse hats you find that the average distance between the ears on the hats is 5.2 inches with a standard deviation of 1 inch.
A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Unfortunately, the reliability of this test is only 80%, which means that 20% of the tested will get a false positive.
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Each home was 24 and the standard deviation of the sample was 5 people. Develop a 98 percent confidence interval for the population mean.
Write the null and alternative hypotheses for testing if participants and non-participants differ in level of problem behavior (Y).
A random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find the probability that exactly 3 experienced insomnia as a side effect.
assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of 2275
lay out the design for two between-subjects experiments a an experiment involving an experimental group and a control
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