There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re- quest. The server can only serve one request at a time, and will serve a request completely before serving other requests. The service times of different requests are independent exponentially distributed random variables with parameter μ, and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state distribution of the number of pending requests, including the one presently served, if any.
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- In a system with a single capacity 1 server with Random.Exponential(0.25) minutes inter-arrival time and Random. Triangular(.1,.2,.3) minutes processing time, what is the expected server utilization?ion 19 of 23 The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 54 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29μ=28.29 and ?=33.493σ=33.493, respectively. Let ?X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯x¯. Use the CLT again to determine the probability that the mean taxable wages in James' sample of 54 counties will be…Trematodes of the species Euhaplorchis californiensis may infect the California kill fish, Fundulus parvipinnis. Researchers have observed that infected fish spend excessive time near the water surface, where they may be more vulnerable to bird predation. Researchers set up an experiment in a large outdoor tank that stocked with three kinds of killifish, uninfected, lightly infected, and highly infected, and recorded the number of fish that is eaten by birds. State the null and alternative hypothesis
- A report by the New York Times in 2022 indicated that, on average, a married woman in the United States goes out with her female friends an average of 5.7 times peryear. A student at Century College conducts a study of her own by randomly surveying married women in White Bear Lake and obtained this data for the number of times in a year: 3 1 1 3 7 2 9 4 6 4 3 8 0 5 6 4 0 1 3 0 Use your calculator to determine the mean and standard deviation for this sample. Then, at the level of significance, Test the claim that married women in White Bear Lake, on average, go out with their female friends less than the overall national average. Be complete, show every step including hypotheses, a labelled graph, and clearly state the final result. Do not use the P-value method. Explain what the final result means in the context of this problem.The viruses causing problems in strawberry plants are mainly spread by one insect, the strawberry aphid. Carly believes that as aphids feed on leaves, they transmit viruses that can cause a rapid decrease in plant growth. She decides to verify whether or not the number of strawberry aphids found on a plant could be linked to its growth. She therefore randomly chooses 5 strawberry plants at the same stage of development in a virus-infested garden. For each individual plant, she first collects all the aphids present on the plant and weighs them, and then weighs the entire plant to have a measure of plant growth. She obtains the following data. (Attach on side) Is Carly correct in thinking that when the number of aphids on a plant is larger, the growth of the plant is affected (i.e., its weight is smaller)? Apply the appropriate statistical method with a test of significance at α = 0.05.A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n = 10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all. The dependent variable is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. (Hint: start with the df column). Source SS df MS Between ___ ___ 15 F = 7.50 Within ___ ___ ___ Total ___ ___
- An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 70% chance of moving to the high-risk category the next year and a 30% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.)A pharmaceutical company has developed a drug that is expected to reduce hunger. Totest the drug, three samples of rats are selected with n = 9 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Slart with the df column.) s.s. df. M.S. F Between 3.65 Within 3.12 TOTAL Use the =FDIST() function in Excel to locate the pvalue for this ANOVA: pvalue - Report p-value accurate to at least 6 decimal places. If you use a significance level of a = .05, what would you conclude about these treatments? OThere is a significant difference between treatments OThese data do not provide evidence of a difference between the treatmenESIn various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a two- sample t-interval. COINS (21.MWX Two-Sample T-Test and CI: Coin1, Coin4 A COINS (2)MWX Two-Sample T-Test and Cl: Coin4, Coin1 Method Method mean of Coin1 Pa mean of Coind Difference u- 4 mean of Coin4 z mean of Coint Difference: - Vz Equal variances ore assumed for this analysis Equal variances ore assumed for this…
- A disk drive has a constant failure rate and an MTTF of 5000 hr. (a) What will the probability of failure be for one year of operation? (b) What will the probability of failure be for one year of operation if two of the drives are placed in active parallel and the failures are independent? (d) What will the probability of failure be for one year of operation if the system si changed to standby model. (e) Describe the effect on the MTTF with a switching failure probability of 0.05. () What would be change in MTTF if the probability of failure of standby unit is 10 percent of the failure of the primary unit in the standby mode?A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=9 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 4.36 Within 3.71 TOTAL Use the =FDIST(∙) function in Excel or the pf(∙) function in R to locate the p-value for this ANOVA:p-value = Report answer accurate to at least 4 decimal places.If you use a significance level of α=.05, what would you conclude about these treatments? There is a significant difference between treatments These data do not provide…A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n = The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1- month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) 8 in each sample. S.S. d.f. M.S. F Between 7.22 Within 3.51 ТОTAL