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We consider a discrete-time Markov chain whose state space is the set {0,1,2} and whose one-step transition probability matrix is
We say that a renewal took place when the initial state 0 is revisited.
(a) What is the average number of transitions needed for a renewal to take place?
(b) Let N{t), for t > 0, be the number of renewals in the interval [0, t], where t is in seconds. If we suppose that every transition of the Markov chain takes one second, calculate
Using data from Boston, Massachusetts, a test of independence is run on the claim that ice cream sales per month and the number of car wrecks per month are independent. The claim is rejected.
consider the following simple model for daily changes in the price of a stock. suppose that on each day the price
A shipment of 500 dolls is received by Panda Importers. The quality control manager selects a random sample of 75 to test. Five are bound to be defective. Construct a 90 percent confidence interval for the population proportion of defective dolls ..
What would be your best point estimate for average Sales in weeks for which Newspaper advertising were $1 million? What would be an appropriate interval estimate for this?
Advertising agency. The managing partner of an advertising agency is interested in the possibility of making accurate predictions of monthly billings. Monthly data on amount of billings (Y. in thousands of constant dollars) and on number of hours ..
the mean weight on my sons football team is 185 pounds with a standard deviation of 20 pounds. determine the standard
(a) Find the lower and upper quartiles, median, and interquartile range. Check for any outliers and interpret. (b) Construct a box plot and interpret. (c) Are there any outliers?
A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. Correlation as a statistic cannot explain why or how the relationship between two..
Find out the probability that at least one of the CD's is defective?
According to a national CNN/USA/Gallup survey of 1,025 adults, conducted March 14-16, 2008, 63% say they have experienced a hardship because of rising gasoline prices. How do you believe the survey was conducted and what types of bias could occur ..
What types of sources of capital can be employed in a transaction? Pick a single source of capital and describe why/under what circumstance you would use this type source.
Determine the distribution of the data by using the Goodness of Fit Test - Determine the parameters of the distribution by using the probability plot method.
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