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1. Toss a fair die repeatedly. Let Sn denote the total of the outcomes through the nth toss. Show that there is a limiting value for the proportion of the first n values of Sn that are divisible by 7, and compute the value for this limit. Hint : The desired limit is an equilibrium probability vector for an appropriate seven state Markov chain.
2. Let P be the transition matrix of a regular Markov chain. Assume that there are r states and let N (r) be the smallest integer n such that P is regular if and only if PN (r) has no zero entries. Find a finite upper bound for N (r). See if you can determine N (3) exactly.
Sources and Uses of Cash. State how each of the following events would affect the firm's balance sheet. State whether each change is a source or use of cash.
binary signals are transmitted at a constant rate of 1000 per second. suppose that transmission errors occur
How many cans of paint should the sample contain if the researcher wants to be 98% certain of being within one percentage point of the true proportion of this chemical?
Using the full 5-step process test to see if a population mean is not 25. Sample data is: Mean 24, standard deviation 10 and a sample of 400 was taken.
This second sample had an average response of 132 with a sample variance of 16. What is the pooled standard deviation for this problem?
A random sample of 4000 U.S. citizens yielded 2190 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.
Develop a point estimate of the number of minutes per day officeworkers waste trying to locate mislabeled, misfiled, or misplaced items.
the independent newspaper tabulated the gender of all candidates running for election in the 1992 british general
Create a 95% confidence interval for the population mean days absent for sickness based on this sample. Select the answer closest to your results.
Let's further suppose that there was good interrater reliability on these frequency counts of behaviours and that they are interval/ratio level of measure, normally distributed, and independent observations.
Find the probability that a random selection of 9 songs will have mean length of 186.30 seconds or less. Assume distribution of the lengths of the songs is normal.
As the financial manager of ABC computers, you are ready to make some decisions. You are trying to see where revenues are going?is the company ready to expand, and if so, when?
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