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1. Three white and three black balls are distributed in two urns in such a way that each contains three balls. We say that the system is in state i, i = 0, 1, 2, 3, if the ?rst urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the ?rst urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why {Xn, n = 0, 1, 2, .. .} is a Markov chain and calculate its transition probability matrix.
2. Suppose that whether or not it rains today depends on previous weather conditions through the last three days. Show how this system may be analyzed by using a Markov chain. How many states are needed?
Flu cases this past fly season in the Central City school system were about 15 per week. For the entire state, the weekly average is 16 and the standard deviation, 2.35. Are the kids in Central City as sick as the kids throughout the state?
We have a box of 12 light bulbs. The probability that a particular light bulbs lights on opening is 0.95. This meets the binomial assumptions. Find the probability that 9 light bulbs light up.
Listed below are altitudes (thousands of feet) and outside air temperatures(degrees Fahrenheit) recorded by the author during Delta Flight. is there sufficient evidence to conclude that is a linear correlation between altitude and outside air temp..
Compute the population mean, the population median, the population midrange, the population range, the population variance, the population standard deviation, and the population proportion of odd numbers. Verify the following results:
Assuming that the data may be viewed as a random sample from a normal population, construct a 99% con?dence interval for the actual variance of the air pollution index for this city and interpret.
The annual mean vehicle miles of travel per household
the function fx0 for xlt0 14x6 for 0ltxlt2 1 for xgt2 is the distribution function of a mixed random variable x.
Find the 90% confidence interval for the variance and standard deviation of the ages of seniors at oak park college if a sample if 24 students has a standard deviation of 2.3 years.
In a sample of 100 M&M's, it is found that 8% are brown. Use a 0.05 significance level to test the claim that of the Mars candy company that the percentage of brown M&M's is equal to 13%. Identify the null and alternative hypotheses. Find the tes..
in a recent study researchers followed 104000 u.s. veterans who had served in the armed forces and a comparison group
Probability randomly selected person from US who is certain or has little doubt has no more than a H.S. education? probability randomly selected person from US will be a C.G. and be "certain" or "little doubt"?
Of a random sample of 600 trucks at a bridge, 114 had bad signal lights. Construct a 95 percent confidence interval for the percentage of trucks that had bad signal lights.
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